NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Introduction

The number is an idea which has different meanings according to the way we use them.

• The number is made up of digits and has different values or numerals.
• The number system helps us to group numbers according to their properties.
• Place value and face value of numbers help us to define the numbers and arrange them in ascending or descending order.
• Understanding the value of a number helps in comparing numbers.

Vishal was a new student in the class. The class teacher asked him to introduce himself.

You can see that like Vishal, we use so many numbers in our daily life, which have different meanings years refers to the age of Vishal and 37 refers to the door number of his house. Let us get to know about numbers.

Read and Learn More Class 3 Workbook Solutions

NCERT Workbook Solutions For Class 3  Chapter 1 Number System

Digits are single units that form the numeral. They are 0, 1, 2, 3, 4, 5, 6,7, 8, 9.

DecimaI number system or the Hindu-Arabic number system, the numbers are symbols or digits from zero to nine (0, 1, 2, 3, 4,5,6,7,8,9).

A system is the grouping of similar things based on a few rules. Let us see how numbers are grouped in a system.

• Natural Number System: All countable numbers from one to infinity are called Natural numbers. Natural numbers are denoted by the symbol ‘N’.
• Counting (Natural) Numbers: 1,2,3, 4,5…
• Whole Number System: The teacher asked a very interesting question to Vishal. “Vishal, can you tell me how old you were, on the day you were born?” What do you think will be Vishal’s answer? “Zero”! Zero is a very interesting number. lt can mean nothing or it can mean a very large value depending on where it is written.
• Zero, together with natural numbers forms the Whole number System.
• Whole Numbers: 0, 1, 2, 3, 4, 5…
• Place value of numbers: Place value gives the value of a numeral based on its position in a number. Their values are determined from right to left as ones, tens, hundreds, thousands, ten thousand, etc.

Vishal has collected 157 stamps. Let’s find the value of this numeral.

157 = 100 + 50 + 7 (One hundred, five tens and seven ones)

Place value of numbers Example:

2574 = 2000 + 500 + 70 + 4 (Two thousand five hundred and seventy-four)

55023 = 50000 + 5000 + 0 + 20 + 3(Fifty-five thousand and twenty-three)

Face value of numbers: The value of a digit in a number is called its face value. The face value of a number remains the same irrespective of its position.

Face value of numbers Example:

1. The face value of 7 in 157 is seven and its place value is seven ones.
2. The face value of 7 in 2574 is seven and its place value is seventy.

NCERT Workbook Solutions For Class 3  Chapter 1 Number System

Question 1. Choose the correct alternative.

1. How many 10 do you need to make 1000?

1. 100
2. 50
3. 20
4. 10

Answer:

2. The expanded form of 705 is

1. 70+5
2. 7+5
3. 700+5
4. 7+0+5

Answer:

3. The number just after 100 is

1. 101
2. 99
3. 110
4. 111

Answer:

4. The smallest two-digit number is

1. 11
2. 22
3. 10
4. 99

Answer:

5. The number, one less than 66 is

1. 61
2. 65
3. 67
4. 55

Answer:

Question 2. Match the Column-1 with Column-2.

1. (1) (C), (2) (D), (3) (A), (4) (B)
2. (1) (A), (2) (D), (3) (C), (4) (B)
3. (1) (B), (2) (A), (3) (D), (4) (C)
4. (1) (C), (2) (D), (3) (B), (4) (A)

Answer:

Question 3. State whether the following statements are true or false.

1. The face value of 8 in 489 is 8. ()

2. The place value of ‘t’ in 415 is one ()

Answer:

Question 4. Fill in the blanks.

1. 100, 102, __, 106, __,110.
Answer:

2. 5507=5000+ __ +7.
Answer:

Question 5. Very Short Answer Type Questions.

Find out the value of numbers, place values, and face values of the following:

1. 4 in three thousand four hundred and fifty-six.

Number:

Place Value:

Face value:

Answer:

2. 6 in five thousand and sixtY-two.

Number:

Place value:

Face value:

Answer:

Question 6. Short Answer Type Questions.

1. How many hundreds are there in 8000? What is the face value and place value of 8 in 8000?
Answer:

2. Write the expanded form of 40732. How many thousands are there in this number?
Answer:

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Activity Corner

Identify the number.

Expanded form: ______

Standard form: ______

Place value of 1: ______

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Ordering Numbers

Ascending order is arranging numbers from the smallest to the greatest value.

• Descending order is arranging numbers from greatest to the smallest value
• Learn to write numbers in ascending and descending order.

Look at these two sets of Chennapatna organic wooden toys. The dolls in picture A can be stacked one inside the other when you arrange them from smaller size to bigger size.

ln picture B, the wooden rings are arranged from bigger to smaller to create a beautiful toy. Have you seen these toys?

Ascending order: Arrange the numbers from smaller values to greater values.

Ascending order Example:

1. 400,25, 1,60, 45,5003.

Ascending order: 25<45<L60< 400< 5003.

2. 4005, 2003,3004,1001.

Ascending order: 1001 < 2003 < 3004 < 4005.

Descending order: Arranging the numbers from greater value to the smaller value.

Descending order Example:

1. 8481,8850, 8586, 8611, 8516.

Descending order: 8850 > 8611 > 8586 > 8516 > 8481.

(These are the heights of the five tallest mountains of the world (in metres), with the tallest being Mount Everest at the height of 8850 meters.)

2. 5432, 2922, 2656, 7749.

Descending order: 7749 > 5432> 2922> 2656.

Predecessor and Successor:

We can find the predecessor and successor of every number in the whole number system.

Predecessor of a number is a number which comes just before it or a number which is one less than the number.

Predecessor of a number Example:

Predecessor of 9 = 8 (9 – f = a)

Predecessor of 100 = 99 (100 – 1 = 99).

(Observe that ‘zero’ does not have a predecessor.)

Successor of a number is a number which comes just after it or a number which is one more than the number.

Successor of a number Example:

Successor of 500 = 501 (500 + 1 = 501).

Successor of 9999 = 10000 (9999 + l- = 10000).

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Ordering numbers

Question 1. Choose the correct alternative.

1. The ascending order of 51, 41, 21, 61 is

1. 21 <41<51 <61
2. 61 <51 <41<21
3. 21 > 41 > 51 > 61
4. 41 < 21 < 61 < 51

Answer:

2. The sum of the predecessor and successor of 100 is

1. 102
2. 100
3. 200
4. 300

Answer:

3. The difference between a number and its successor is always

1. 1
2. 2
3. 5
4. 10

Answer:

4. Choose the correct one arranged in descending order.

1. 3<6<9<12
2. 100<200<300<400
3. 99>89>79>69
4. 22<32<42<52

Answer:

5. The difference between 99 and its successor is

1. 5
2. 4
3. 2
4. 1

Answer:

Question 2. Match the Column-1 with Column-2.

1. 1 (D), 2 (E), 3 (A), 4 (B), 5 (C)
2. 1 (C), 2 (E), 3 (A), 4 (B), 5 (D)
3. 1 (C), 2 (B), 3 (E), 4 (A), 5 (D)
4. 1 (C), 2 (A), 3 (E), 4 (B), 5 (D)

Question 3. State whether the following statements are true or false.

1. 1. 2003 is greater than 2030 ()
2. 2. The successor of 972 = 972 + 1 ()

Answer:

Question 4. Fill in the blanks.

1. ___ <355< ___ < 365
Answer:

2. ___ <99< ___ < 9999
Answer:

3. ___ <707 < ___ < 709
Answer:

Question 5. Very Short Answer Type Questions.

1. Number of trees in five different parks in the city – 111, 101,11,110. Arrange in ascending order.

Answer:

2. Number of schools in five districts – 415,455,405,445. Arrange in ascending order.

Question 6. Short Answer Type Questions.

1. The following are the temperatures recorded in different cities. Arrange them in descending order.

36°C, 45°C, 39°C, 44°C, 32°C

Answer:

2. Write the following set of numbers in descending order.

Answer:

Question 7. Activity Corner

1. Identify the missing number.

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Comparing Numbers

Once we understand the value of numbers, we can write the greatest and smallest number from the given digits and can easily compare two or more digits.

Writing the greatest and smallest number from the given digits

Follow the simple rules :

1. Write the given digits in ascending order.
2. For the greatest number, write the digits from the highest value to the lowest value.
3. For the smallest number write the digits from the lowest value to the highest value. We will start with a digit other than 0 and write the 0 in second place.
4. ln case, there are two equal digits, then write them at consecutive places.

Comparing Numbers Examples:

Question 1. Write the greatest number that can be formed with digits 9, 3.
Answer: Ascending order 3 < 9.

The greatest number that can be formed is 93 (ninety-three).

Question 2. Write the greatest number that can be formed with digits 7, 3, 5.
Answer: Ascending order 3 <5 < 7.

The greatest number that can be formed is 753 (seven hundred and fifty-three).

Question 3. Write the smallest number that can be formed with 8, 4.
Answer: Ascending order 4 < 8.

The smallest number that can be formed is 48 (forty-eight).

Question 4. Write the smallest number that can be formed with 2, 1, 3.
Answer: Ascending order 1<2<3.

The smallest number that can be formed is 123 (one hundred and twenty-three).

Rounding off numbers

Imagine this, you are shopping in a supermarket and have bought two items. You want to do a quick check of the approximate value. This is where your place value comes in real handy. How?

Let the cost of items be, ₹ 97, < ₹ 228.

The best and easiest way to add is by splitting them according to their place values.

₹97 is nearest to 100

₹212 is nearest to 210

The approximate total will be ₹ 310. (Actual value is ₹309)

Rounding off to the nearest 10

Follow the rules:

1. Check the digit in one’s Place.
2. If it is <5, round it off to less than ten.
3. If it is >5, round it off to the higher ten.

Rounding off to the nearest 10 Examples:

1. Round off t2 to the nearest ten. 2<5, it is closer to 10 than twenty. So, 12 is rounded off to 10.
2. Round off 97 to the nearest ten. 7>5, it is closer to L00 than 90. So, 97 is rounded off to 100.

Rounding off to the nearest 100

Follow the rules:

1. Check the digit in tens Place.
2. If it is <50, round it off to lesser hundred.
3. if it is >50, round it off to the higher hundred

Rounding off to the nearest 100 Examples:

1. Round off 212 to nearest hundred. 12<50,2I2iscloserto hundred than 200. So, 2t2is rounded offto 200.
2. Round off 387 to nearest hundred. 87 > 50, 387 is closer to 400 than 300. So, 387 is rounded off to 400.

NCERT Workbook Solutions For Class 3  Chapter 1 Numbers Comparing Numbers

Question 1. Choose the correct alternative.

1. The smallest possible number that can be written with the digits 1,7, 1, is

1. 177
2. 117
3. 171
4. 711

Answer:

2. The largest possible number that can be written with the digits 0, 5, and 5 is

1. 505
2. 55
3. 50
4. 550

Answer:

3. The number of children in 3 sections of class 5 is 32, 36, and 37. The total number of children to the nearest ten is

1. 120
2. 105
3. 90
4. 110

Answer:

4. 68 rounded off to the nearest ten and hundred will be

1. 50, 100
2. 60, 100
3. 70, 100
4. 70,200

Answer:

5. The numbers 144 and 164 rounded off to the nearest hundred will be

1. 100,100
2. 100,200
3. 200, 100
4. 140,160

Answer:

Question 2. Match the Column-1 with Column-2.

1. 1(D), 2(E), 3(A), 4(B), 5(C)
2. 1(C), 2(E), 3(A), 4(B), 5(D)
3. 1(E), 2(D), 3(B), 4(C), 5(A)
4. 1(C), 2(D), 3(B), 4(A), 5(E)

Answer:

Question 3. State whether the following statements are true or false.

1. 3045 is the smallest possible number with the digits 5,3,0,4 ( )
2. 9810 is the largest possible number with the digits 0, 9, 1, 8 ( )

Answer:

Question 4. Fill in the blanks.

1. The smallest five-digit number is ___ and its successor is -.
2. ___ is the largest 3-digit number and its predecessor is -.

Answer:

Question 5. Very Short Answer Type Questions.

1. 1,6,1,8,2

Largest possible number ____

Smallest possible number ____

Answer:

2. 7,3,5,9,0

Largest possible number ____

Smallest possible number ____

Answer:

Question 6. Short Answer Type Questions.

Question 7. Activity Corner

ln a school, each class was asked to collect newspapers for recycling. The contributions from different classes were as follows. Estimate to the nearest ten, how many new papers were collected approximately?

NCERT Workbook Solutions For Class 3 Chapter 2 Number Operations (Addition and Subtraction) Introduction

Adding two or more numbers is to find how many we have in all. The numbers we add are called the addends and the answer is the sum.

• When we add one to a number, the answer is its Successor. Adding a number to itself gives it double.
• Subtracting is taking away from a number. The answer we get is called the difference of the two numbers.
• When we subtract one from a number, the answer is its predecessor.
• When we add or subtract zero to a number, the number remains the same.

Read and Learn More Class 3 Workbook Solutions

NCERT Workbook Solutions For Class 3 Chapter 2 Addition and Subtraction

The Art Teacher divided the class into groups for a project. One of the groups decided to do crafts with shells. They had a good collection of colorful shells in different shapes.

Anu gave 14 shells, Vishal gave 16 shells, Preetigave 25 shells.

Manu gave 10 shells and Ria gave 8 shells. How many shells do they have in all? We add the numbers to get the sum or total number of shells.

How many shells do the children have in total?

14 + 16 + 25 + 10 + 8 = ?

14 + 16 = 30

30 + 25 = 55

55 + 10 = 65

65 + 8 = 73

The children had a total of 73 shells.

How much is 73 less than 100?

100 – 73 = 27.

Note: Addition and Subtraction are inverse operations.

Addition And Subtraction Example: 5 + 4 = 9, 9 – 5 = 4 and 9 – 4 = 5

We have learned how to add two-digit numbers. Numbers can be grouped according to their place value, to make addition easier. Let us see adding tens to make them hundred and thousand.

Adding without carrying over

Question 1. 160 + 20 = ?

Question 2. 130 + 2450 = ?

Question 3. Add 1374 + 222 + 4101 = ?

Subtraction without borrowing

Question 4. 170 – 30 = ?

Question 5. 5730 – 2530 = ?

Example 6. Subtract 2032 from 9254

NCERT Workbook Solutions For Class 3 Chapter 2 Number Operations Addition and Subtraction

Question 1. Choose the correct alternative.

1. 20 + 40 + 130 = ?

1. 100
2. 160
3. 180
4. 190

Answer: 4. 190

2. The sum of 100 + 120 + 140 is

1. 360
2. 320
3. 340
4. 300

Answer: 1. 360

3. Add: 1200 + 200 + 2 = ?

1. 1222
2. 1202
3. 1400
4. 1402

Answer: 4. 1402

4. Subtract: 450 – 230 = ?

1. 220
2. 250
3. 230
4. 120

Answer: 1. 220

5. 7777 – 300 = ?

1. 7200
2. 7270
3. 7477
4. 7300

Answer: 3. 7477

Question 2. Match the Column-1 with Column-2.

Answer: (1) → B, (2) → C, (3) → D, (4) → A

3. Fill in the blanks.

1. 530 + ___ = 2590
2. 180+ ___ +1000=1690

Answer: 

4. State whether the following statements are true or false.

1. 5105 + 550 = 5655
2. 2340 – 120 = 2220
3. 270 – 50 = 230

Answer:

1. 1. 5105 + 550 = 5655 statement is true
2. 2. 2340 – 120 = 2220 statement is true
3. 3. 270 – 50 = 230 statement is false

5. Very Short Answer Type Questions.

1. 700 + 200 = 450 + ___
2. 500 + 300 = 300 + 300 + ___

Answer:

6. Short Answer Type Questions.

1. 100 – 50 = ____ = 30 + ____
2. 180 – 0 = ____ = 100 + ____

Answer:

1. 100 – 50 = 50 = 30 + 20

2. 180 – 0 = 180 = 100 + 80

7. Activity Corner

1. Solve the following puzzle using addition and subtraction.

2. Complete the hexagon wall. Each number is made by adding the two numbers below.

Carryover and Borrowing Numbers

Addition with carry-over:

To add two-digit numbers, follow these rules:

• Write the number one below the other under the respective place value. Ones below ones and tens below tens.
• Add the one’s place.
• If the answer is less than L0, write it under the one’s Place.
• If the answer is more than L0 or more, it is a two-digit number. Write the value of the one under one’s and carry over the ten’s value to the ten’s place
• Now add the digits in ten places and write the value. The answer is the sum of the two numbers.

Question 1. Add 72 and 57.

Question 2. Add 465, 828 and 42

Subtraction by borrowing:

To subtract two-digit numbers, follow these rules:

• Write the numbers one below the other; under the respective place value. Ones below ones and tens below tens.
• Start from left, subtract the one’s place.
• If the first number (number on top) is greater than the second number; subtract and write in the one’s place.
• If the first number (number on top) is Iesser than the second number, borrow a ten from the ten’s column. Subtract the numbers and write in the one’s place.
• Now subtract the digits in ten’s place and write the value. The answer is the difference of the two numbers.

(Note: Remember to subtract the smaller number from the bigger number.)

Question 3. Subtract 17 from 35.

Answer: 35 – 17 = 18

Question 4. Subtract 75 from 120.

Answer: 120 -75 = 45

Question 5. Subtract 2759 from 6342.

Answer: 6342 – 2759 = 3583

NCERT Workbook Solutions For Class 3 Chapter 2 Number Operations Carryover and Borrowing Numbers

Question 1. Choose the correct alternative.

1. 6130 – 1799 = ?

1. 4229
2. 4331
3. 4631.
4. 5131

Answer: 2. 4331

2. 6612 – 446 = ?

1. 3166
2. 2166
3. 61,66
4. 5166

Answer: 3. 6,166

3. 1190 + 1009 + 999 = ?

1. 3198
2. 3138
3. 3130
4. 3090

Answer: 1. 3198

4. 2599 + 511 + 250 = ?

1. 2460
2. 3560
3. 3660
4. 3360

Answer: 4. 3360

5. 8612 + 9446 = ?

1. 18058
2. 17058
3. 1058
4. 1778

Answer: 1. 18058

Question 2. Match the Column-1 with Column-2. 

Solution. (1) → D, (2) → E, (3) → B, (4) → C, (5) → A

Question 3. State whether the following statements are true or false.

1. If 84 – 16 = 68 then 184 – 116 = 68. ()
2. If 13 – 7 = 6 then 7 + 6 = 13. ()
3. 200-199 = 199-200 ()

Answer:

1. If 84 – 16 = 68 then 184 – 116 = 68. The statement is true.
2. If 13 – 7 = 6 then 7 + 6 = 13. The statement is true.
3. 200 – 199 = 199 – 200. The statement is false.

Question 4. Very Short Answer Type Questions.

1. Find the sum of 148 and 335.
Answer: 148 + 335 = 483

2. Find the difference of 850 and 405.
Answer: 850 – 405 = 445

3. Find the sum of 99,999 and 9999
Answer: 99,999 + 9999 = 1,09,998

4. Subtract: 3700 – 555
Answer: 3700 – 555 = 3,145

Question 5. Activity Corner

1. Find the code with the given clue.

270 – 90 = O

180 + 243 = B

250 – 160 = A

270 + 144 = R

700 – 350 = V

NCERT Workbook Solutions For Class 3 Chapter 2 Number Operations Word Problems-Addition and Subtraction

We use addition and subtraction very often in our life. Let us understand when to add and when to subtract, in each situation.

Identify the keywords.

To solve word problems in addition or subtraction,

• First, identify the keywords and decide on the operation (addition or subtraction).
• Second, write down the numbers and group them according to Place value.
• Third, solve the sum by adding or subtracting the numbers.
• Use carryover in addition and borrowing in subtraction wherever necessary.

Addition Word Problems

Question 1. Amitha went with her mom to the nursery to buy saplings for their garden. They bought marigold saplings for ₹166, petunias for ₹280, poppies for ₹275, and Jasmin for ₹390. How much should they pay for all the saplings?

Question 2. Chitra and her brother Satish like to read books. They have L2 books on magic, 8 books on craft making, 32 books on comics, and 27 coloring books. How many books do they have combined?

Subtraction Word Problems

Question 3. Swamp deer population at Assam’s Manas National Park has been recorded as 121 in 2021, from 99 in 2020. What is the difference in the count of deer?

Question 4. The number of volunteers who registered in a summer camp to clean the beach was 2465. lf 826 of them were adults and the remaining were school students. How many students had registered as volunteers?

NCERT Workbook Solutions For Class 3 Chapter 2 Number Operations Word problems – Addition and Subtraction

Question 1. Choose the correct alternative.

1. I am the sum of two centuries and a half-centurys. Who am I? (Hint: a century is 100)

1. 250
2. 300
3. 150
4. 200

Answer: 1. 250

2. If you remove 220 from 10OO you will get.

1. 880
2. 780
3. 760
4. 860

Answer: 2. 780

3. The number of participants from each school for the district sports meet was increased from 450 to 800. What is the exact difference in student numbers?

1. 400
2. 1250
3. 350
4. 850

Answer: 3. 350

4. The number of visitors to the museum in the month of April was adults 130, students 480 teachers 140, and foreigners 125. How many visitors visited the museum in total?

1. 680
2. 770
3. 920
4. 875

Answer: 4. 875

5. What do you get when you take away 870 from 2654?

1. 1784
2. 2024
3. 1874
4. 1984

Answer: 1. 1784

Question 2. Match the Column-1 with Column-2.

Solution. (1) →E, (2) → C, (3) → A, (4) → B, (5) → D

Question 3. State whether the following statements are true or false.

1. When you add zero to any number the value does not change’ ( )

Answer: True

2. When you subtract zero from any number, its value decreases’ ( )

Answer: False

Question 4. Very Short Answer Type Questions.

Ravi and his sister Radha were playing the snake and ladder game during their holidays’ They played five games and the score was:

Ravi: 12, 80, 40, 11, 33

Radha: 63, 46, 100, 32, 77

1. What is Ravi’s total?

Answer: 12 + 80 + 40 + 11 + 33 = 176

2. What is Radha’s total?

Answer: 63 + 46 + 100 + 32 + 77 = 318

3. Who won the game and by what score?

Answer: Radha

Question 6. Activity Corner

1. A magic square is where you get the same value when you add horizontally each row, and vertically each column

NCERT Workbook Solutions For Class 3 Chapter 4  Chapter 4 Measurement

Concept Review Introduction

Measurement can be defined as giving a numerical value to an attribute or property like length, distance, weight capacity, etc.

• Different tools are used for measuring different attributes.
• Without the numerical measurement, we can only give a general comparison of properties.
• Units of length are meter (m), kilometer (km), centimeter (cm), millimeter (mm).
• Units of weight are milligrams (mg), grams (g), and kilogram (kg).
• Units of capacity or volume are liter (L) and millilitre (mL).

Read and Learn More Class 3 Workbook Solutions

NCERT Workbook Solutions For Class 3 Chapter 4  Measurement Measuring Length

Length is the end-to-end stretch measure of an object or distance using a tool according to standards. Length helps us to understand, what is short, long, near, or far?

Comparing Length

When we know the length of two objects, we can compare them easily.

To exactly say in numbers, how long and short, how tall and short, or how far and near, we use measurements of length.

Length

The length of an object is a measurement of its longest side.

The length of the pencil is 14 cm on the scale.

The height of a person can be measured by using a measuring tape or a scale.

The height of the person is 166 cms, as shown in the scale.

Tools used for measuring length

ln previous days, humans used their hands and feet to measure length.

• A ruler is used to measure shorter lengths. (For example: Length of a pen, length of a book, length of the Laptop screen)
• A tape is used for measuring greater length. (For example: Length of table, cloth, room.)
• A surveyor’s tape or GPS measuring devices are used to measure distances. (For example: Distance between two cities, distance from your house to the market.)

Units of measuring length

The standard unit for measuring length is Metre, usually written as ‘m’. it can be broken down into smaller units as shown below:

• 1 metre (1 m) = 100 centimetres (100 cm)
• 1 centimeter (1 cm) = 10 millimeters (10 mm)
• Long distances are measured in kilometers (km).

1 kilometre (1 km) = 1000 metres (1000 m)

Observe your ruler.

A scale is divided into units of centimeters. 1 cm is divided into 10 smaller units of millimetre.

Unit conversions

The changing of standard units from one form to another is called conversion. This helps us to calculate and understand the length easily.

Question 1. In the picture of the scale shown above, what is the length of the scale in millimeters (mm)?
Answer: 1 cm = 10 mm

15cm=15 × 10 = 150 mm

The length of the scale is 150 mm or 15 cm.

Question 2.

Convert the following:

1. 5m to cm
Answer:

1m = 100cm

5m = 5 × 100 = 500cm

2. 2 km to m
Answer:

1 km = 1000 m

2 km = 2 × 1000 = 2000 m

3. 1 km to cm
Answer:

1km = 1000m

1m = 100cm

1000m = 1000 × 100cm

= 100000 cm

NCERT Workbook Solutions For Class 3 Chapter 4  Measuring Length

Question 1. Choose the correct alternative.

1. 5 metres = ___ cm

1. 50
2. 500
3. 5
4. 5000

Answer: 2. 500 cm

2. 7000 m = ___ km

1. 7 km
2. 70 km
3. 700 km
4. 7000 km

Answer: 1. 7 km

3. Which of these will be in kilometers (km)?

1. Length of a curtain
2. Distance from your home to school
3. Distance from the kitchen to the front door
4. Length of table

Answer: 2. Distance from your home to school

4. Which of these will be measured in meters (m)?

1. Length of paper
2. Mobile screen
3. Length of a curtain
4. Television screen

Answer: 3. Length of a curtain

5. Which of these will be measured in centimeters (cm)?

1. Distance of 2 cities
2. Length of a river
3. Length of a playground
4. Length of a paper

Answer: Length of a paper

Question 2. Match the Column-1 with Column-2.

Answer. (1) → B, (2) → D, (3) → A, (4) → E, (5) → C

Question 3. State whether the following statements are True or False.

1. The length of a spoon will be measured in meters. 

Answer: True

2. The size of a room will be measured in kilometers.

Answer: False

Question 4. Fill in the blanks.

1. 600m+1200m=___ km

Answer: 600m + 1200m = 1.8 km

2. 80cm+70cm+20cm=___ mm
Answer: 80cm + 70cm + 20cm = 1700 mm

Question 5. Very Short Answer Type Questions.

1.

The length of the mobile screen is ___ cms.

Answer: 6 cm

2.

The width of the coin is ___ cms

Answer: 4 cm

Question 6. Short Answer Type Questions.

1. The length of the TV screen is ___ mm which when converted is ___ cms.
Answer: 90.76 cms

2. The breadth of the TV screen is ___ mm which when converted is ___ cms.
Answer: 52.97 cms

Question 7. Activity Corner

1. What is the distance from the Carmel house to the school? Convert the distance in meters.
Answer: 2000 meters

NCERT Workbook Solutions For Class 3 Chapter 4  Measurement Measuring Weight

Weight is the measure of how heavy an object or person is.

• Weight is measured using a tool, according to standards.
• Weight helps us to understand what is heavy and what is light.
• Units of weight are milligrams, grams, and kilograms.

Comparing weight

When we know the weight of two things, we can compare them easily.

Weight

The weight of an object is a measurement of its heaviness.

These 4 bananas weigh 600 grams.

The weight of this banana is 150 gms

The weight of 4 bananas is heavier than 1 banana.

Tools used for measuring weight

Units of measuring weight

The standard unit of measuring weight is kilogram written as kg. It is broken down into the following smaller units.

1 kilogram (1 kg) = 1000 grams (1000g)

1 gram (1 g) = 1000 milligrams (1000 mg)

Weights used for manual calibration

Conversion of units

Conversion of units in weight is done as follows.

Example 1. Convert 5 grams to milligrams.

1 g = 1000 mg

5 g = 5 × 1000 = 5000mg

Example 2. Convert 2 kilograms to grams.

1kg = 1000g

2kg = 2 × 1000 = 2000g

Example 3. Convert 1 kilogram to a milligram

1kg = 1000g

1g = 100 mg

1000g = 1000 × 100

= 100000 mg

Operations on Weight

Adding weights

1. Add 5kg 200g with 9kg 250g.

Answer: 5 kg 200g + 9kg 250g = 14 kg 450g

2. Add 10kg 250g with 7 kg 850g.

Answer: 10kg 250g + 7kg 850g = 18kg 100g

Subtracting weights

3. Subtract 4 kg from 6 kg 500g.

Answer: 6kg 500g – 4 kg = 2kg 500g

4. Subtract 25kg from 75kg.

Answer: 75kg – 25kg = 50kg

NCERT Workbook Solutions For Class 3 Chapter 4  Measurement

Question 1. Choose the correct alternative.

1. 5000 grams is equal to

1. 50 kg
2. 5 kg
3. 500 kg
4. 500kg

Answer: 2. 5 kg

2. 3 kg is equal to

1. 3000 g
2. 30 g
3. 300 g
4. 3 g

Answer: 3000 g

3. 50 g is equal to

1. 500 mg
2. 50 mg
3. 50000 mg
4. 5000 mg

Answer: 3. 50000 mg

4. The approximate weight of a school notebook will be

1. 10 g
2. 250 g
3. 2 kg
4. 3 kg

Answer: 10 g

5. Sum of 200 mg and 800 mg is

1. 1 gram
2. 100 grams
3. 1000 grams
4. 1 kg

Answer: 1. 1 gram

Question 2. Match the Column-1 with Column-2

Look at the weights of different fruits and vegetables given above and select the correct option.

Answer. (1) →B, (2) →E, (3) → D, (4) → C, (5) → A

Question 3. State whether the following statements are True or False.

1. An envelope is lighter than a book.
Answer: True

2. A wooden box weighs lighter than a cardboard box
Answer: False

Question 4. Fill in the blanks.

1. 7 kg = ___ g
Answer: 7000 g

2. 300 g = ___ mg
Answer: 3,00,000 mg

Question 5. Very Short Answer Type Questions.

1. How many 250 g muffins is the same as that of the weight of a 1 kg cake?
Answer: 4 muffins

2. Which weighs more? A bag of 2 kg 600 g of groceries or a bag of 1700 g of groceries.
Answer: 2 kg 600 g

Question 6. Activity Corner

NCERT Workbook Solutions For Class 3 Chapter 4  Measurement Measuring capacity

Measurement of capacity helps us to understand the maximum amount of something, a container can hold.

It is the amount of space available in a container to hold any substance – solid, liquid, or gas.

Capacity

Capacity tells us whether a container can hold more or less of something

Comparing capacity

Quantity and Capacity

The capacity of the three juice bottles is 2 liters.

The quantity of juice in the bottles is empty, half full, and full to its capacity.

Units Of Measuring Capacity

The standard unit of measuring capacity is liters written as ‘L’. It is broken down into the following smaller units.

1 Litre (1L) = 1000 millilitre (1000 mL)

A measuring cup is used to measure capacity.

1 Litre is divided into 10 equal parts.

Each smaller part is 100 ml.

Conversion Of Units

Conversion of units in weight is done as follows.

Example 1.

Convert 2 Litres to millilitres.

1L = 1000mL

2L = 2 × 1000 = 2000 mL

Example 2.

Convert 5000 mL to liters.

1000 mL = 1L

5000 mL = 5000 ÷ 1000 = 5L

Example 3.

There are 5 milk packets of capacity 200 mL each. What is its total capacity in liters?

1 packet = 200 mL

5 packets = 5 × 200mL

= 1000 mL = 1L

NCERT Workbook Solutions For Class 3 Chapter 4  Measurement Measuring Capacity Choose the correct alternative

Question 1. Choose the correct alternative.

1. A bucket can hold 4 liters of water. The amount of water it has, if it is filled to half its capacity will be?

1. 2 litres
2. 4litres
3. 5 litres
4. 10 litres

Answer: 1. 2 litres

2. If 1000 mL = 1 L, then 7000 mL = ?

1. 7000L
2. 700L
3. 7L
4. 70L

Answer: 7 L

3. 500 mL = ___ L

1. \(\frac{1}{2} \mathrm{~L}\)
2. 5 L
3. 10 L
4. 50 L

Answer: 1. \(\frac{1}{2} \mathrm{~L}\)

4. 11 litres = ___ mL

1. 110 mL
2. 11000 mL
3. 1100 mL
4. 1000 mL

Answer: 2. 11000 mL

5. 55L= ___ mL

1. 550 mL
2. 250 mL
3. 5550 mL
4. 55000 mL

Answer: 4. 55000 mL

Question 2. Match the Column-1 with Column-2.

Answer: (1) → B, (2) → C, (3) → A

Question 3. State whether the following statements are True or False.

Answer: 1. False

2. True

Question 4. Fill in the blanks.

1. A 5L bottle is filled with 2500 mL of water. It is filled to ___ of its capacity
Answer: 2500 mL

2. A 1L bottle of water can fill ___ 200 mL water glasses.
Answer: 800 mL

Question 5. Very Short Answer Type Questions.

1. If each of these juice packets contains 500 mL of juice, what is the total quantity of juice available in liters?

Answer: 3 Litres

2. A beaker contains 1 L of liquid, how many 200 mL beakers can be filled with this liquid?
Answer: 5 beakers

NCERT Workbook Solutions For Class 3 Chapter 3 Multiplication And Division Introduction

Multiplication and division are two mathematical operations, which are inverse of each other.

• Multiplication is repeated addition, while division is repeated subtraction of numbers.
• Properties of multiplication are true for any numbers which are multiplied.
• We can find the product of numbers easily using multiplication tables.

Read and Learn More Class 3 Workbook Solutions

NCERT Workbook Solutions For Class 3 Chapter 3 Multiplication And Division Multiplication

Repeated Addition:

Multiplication is the same as the repeated addition of a number. The number which is multiplied is called the multiplicand. The number of times it is multiplied is called the multiplier. The answer is the product.

Consider the following

Question 1.

There are 2 candies in a set, so such sets have 2 + 2 + 2 + 2 + 2= 5 times 2 = 5 x 2 = 10 candies

This is written as

Question 2.

There are 3 cars in a pack, the number of cars in 4 packs will be 3 + 3 + 3 + 3 = 4 times 3 = 4 x 3 = 12

This is written as

Note: Always multiply a number from right to left, starting from one’s place and then moving to ten, hundred, and so on.

Product of a Whole Number

We know that when we multiply two numbers, we get the product. Let us now see the product of a single-digit whole number.

Question 3.

Product of single-digit numbers

Product of 2-digit numbers

Question 4. Multiply 32 × 12

32 ×12 = 384

384 is the product of 32 and 12.

Question 5. Multiply 23 × 42

23  × 42 = 965

966 is the product of 23 and 42.

Note: ln multiplication ‘times’ also stands for ‘groups of’.

3 × 4 (3 groups of 4) is different than 4 × 3 (4 groups of 3) even though their product might be the same.

A times table helps us to remember the multiplication facts

Properties of Multiplication in Whole Numbers

1. The product of ‘0’ (zero) and any number is zero.

2. Multiplicative identity: The product of ‘1’and any number is the number itself (1 × 25 = 25).

3. Commutative property: Changing the order of numbers while multiplying does not change their product.

(2 × 5 = 5 × 2 = 10)

4. Associative property: The product of 3 or more numbers remains the same regardless of how they are grouped.

3 × 5 × 7 = 3 × 5 × 7 = 15 × 7 = 105

3 × 5 × 7 = 3 × 5 × 7 = 3 × 35 = 105

NCERT Workbook Solutions For Class 3 Chapter 3 Multiplication

Question 1. Choose the correct alternative.

1. The multiplication fact for 7 +7 +7 +7 +7 + 7 is

1. 7×6=42
2. 7×7=49
3. 7×4=28
4. 7×1=7

Answer: 1. 7×6=42

2. There are 5 pairs of shoes in a shell the total number of shoes are

1. 5
2. 10
3. 20
4. 12

Answer: 2. 10

3. I bought 3 packets of pens, with 6 pens in each packet. How many pens do I have?

1. 12
2. 6
3. 20
4. 18

Answer: 4. 18

4. The multiplication fact for 90 + 10 = 9 is given by

1. 80+10=90
2. 2×5×9=90
3. 3×3×10=90
4. 10×9=90

Answer:  4. 10 x 9 = 10

5. 4 × 8 = 32 can be written in repeated addition as

1. 8+8+8+8
2. 30+2
3. 15+15+2
4. 20+10+2

Answer: 1. 8 + 8 + 8 + 8

Question 2. Match the Column-1 with Column-2.

Answer: (1) → C, (2) → E, (3) → A, (4) → B, (5) → D

Question 3. State whether the following statements are True or False.

1. If there are 50 eggs in a crate then the total number of eggs in 4 crates will be 200.

Answer. True

2. 2×2×2 is same as 2 × 3.

Answer: False

Question 4. Fill in the blanks.

Complete the repeated addition and write the multiplication facts.

1. 2,4,6,___or 2×4=___.
Answer: 8

2. Skip count by three and fill in the blanks: 27, ___, ___,36
Answer: 30,33

Question 5. Very Short Answer Type Questions.

1. The product of 200 and 6 =

Answer. 1200

2. The product of 10 × 7 × 1 =

Answer. 70

Question 6. Short Answer Type Questions.

Write the Multiplication Fact using the given Array

Answer.  1. 8 x 8 = 64

2. 9 x 6 = 54

Question 7. Activity Corner

1. Complete the multiplication circle.

Answer. 

1. 11 x 0 = 0
11 x 1 = 11
11 x 3 = 33
11 x 5 = 55
11 x 7 = 77
11 x 9 = 99

2. 23 x 0 = 0
23 x 1 = 23
23 x 2 = 46
23 x 4 = 92
23 x 6 = 138
23 x 8 = 184

NCERT Workbook Solutions For Class 3 Chapter 3 Division

The division is one of the four mathematical operations.

• The division is the repeated subtraction of a number.
• Factors are exact divisors of a number.
• Division properties of numbers can also be used as a division strategy

Sharing And Grouping:

The division is the repeated subtraction of a number. The number that is divided is called the dividend and what divides the number; is the divisor.

Question 1. Divide 10 cookies among 2 people.

10 shared among two is 5.

This is written as 10 ÷ 2 = 5,

q = 5 and r = 0

Question 2. Share 21 gifts among 7 people. Put one gift in every box, how many gifts will be there for each of the seven people?

Now we have 21-7 = 14 gifts left

Now we have 1.4-7 = 7 gifts left

7 -7 = 0 all the gifts have been shared among 7 people. Each one gets 3.

or 21 ÷ 7 = 3

This is written as 21 ÷ 7 = 3,

q = 3, r = 0

Question 3.  Share 7 mangoes among 3 people.

7 mangoes are shared among three such that each gets 2 mangoes and 1 is remaining.

2 quotient (q)

This is written as 7 + 3, 3 does not divide 7 completely.

q=3, r=1

Note: Division is equal sharing equal grouping or repeated subtraction.

Factors Of A Whole Number:

A factor divides a number completely without leaving any remainder.

10÷2=5,q=5 and r=0.

Therefore, 2 is a factor of 10.

• 21÷7 = 3, q = 3 r = 0.
• Therefore, 7 is a factor of 21.
• 7 ÷ 3, q = 3, r = 1, 3 is not a factor of 7.
• 1 is a factor of all the numbers.
• Every number is a factor of itself.
• Including 1 and itself, every number has at least two factors.
• A number can have more than two, but a countable number of factors.

Properties of division in Whole Numbers

When we divide a number by 1, the quotient is the number itself.

25 ÷ 1 = 25, 4 ÷ 1 = 4

The division of any number by zero has no meaning.

5 ÷ 0 has no meaning.

When we divide a number by itself, the quotient is 1.

12 ÷ 12 = 1, 100 ÷ 100 = 1

Zero divided by any number gives zero as the quotient.

0 ÷ 1 = 0,0 ÷ 50 = 0

NCERT Workbook Solutions For Class 3 Chapter 3 Division

Question 1. Choose the correct alternative.

1. Rohan shares 30 toffees among 10 friends. How many toffees did each one get?

1. 40
2. 10
3. 3
4. 5

Answer: 3. 3

2. A family of six members paid ₹360 as an entrance fee for the museum. What is the fee for one person?

1. ₹60
2. ₹300
3. ₹30
4. ₹100

Answer: ₹ 60

3. There are 36 students in a class, sitting in 9 rows. lf equal number of them are sitting in each row find the number of students in each row.

1. 12
2. 4
3. 6
4. 9

Answer: 2. 4

4. lf 44 pairs of shoes are arranged equally in 4 rows, how many pairs of shoes are there in each row?

1. 4
2. 8
3. 10
4. 11

Answer: 4. 11

5. When 2 is subtracted nine times from 18, it gives zero. The division fact is written as

1. 18 – 2 = 0
2. 2 × 9 = 18
3. 2 ÷ 18 = 9
4. 18 ÷ 2 = 9

Answer: 4. 18 ÷ 2 = 9

Question 2. Match with Column-1 with Column-2.

Answer. (1) → B, (2) → D, (3) → E, (4) → C, (5) → A

Question 3. State whether the following statements are true or false.

1. 15 + 3 = 3 + 15

Answer. True

2. 37 + 0 has no meaning.

Answer. Fasle

Question 4. Fill in the blanks.

1. There are ___ weeks in 42 days.
Answer: 6 weeks

2. Reeta wants to cycle 15 km in 5 hrs, in 1 hour she cycles ___ km.
Answer: 3

Question 5. Very Short Answer Type Questions.

Question 6. Short Answer Type Questions.

1. 18 cups were arranged in 2 rows with 9 in each row. lf the cups are arranged in 3 rows and 6 rows, how many will be there in each row?

3 × _ = 18, 6 × _ = 18

Answer: 3 x 6 = 18, 6 x 3 = 18

2. The baker baked 20 muffins and 32 lemon tarts. lf she packs an equal number of pieces in each box,

1. How many boxes will she need for a set of 5 muffins?

Answer: 4 boxes

2. How many boxes for a set of 4 tarts?

Answer: 8 boxes

Question 7. Activity Corner

1. Complete the number tile using division facts of 48.

NCERT Workbook Solutions For Class 3 Chapter 3 Multiplication And Division Combined Operation

Multiplication and division are inverse operations.

• We can convert a given multiplication fact to a division fact and a division fact to a multiplication fact.
• To find the value of one item, with a given value of many items – we divide many by one.
• To find the value of many items when the value of one is given, we multiply to find the solution.

Relation between multiplication and division

1. Multiplication and Division are inverse properties of each other.

Question 1.

2. Division by a number is related to multiplication by the same number

Question 2. Change multiplication facts into two division facts.

Application of multiplication and division

Question 3. If the cost of 1 pen is ₹10, what is the cost of 6 pens?
Answer:

Cost of 1 pen = ₹ 10

Cost of 6 pens = 10 + 10 + 10 + 10 + 10 + 10 = 6 × 10 = 60

Question 4. If there are 6 students in a group, how many students are there in 5 such groups?
Answer:

Number of students in 1 group = 6

Number of students in 5 groups = 6 + 6 + 6 + 6 + 6 = 6 × 5 = 30

Question 5. There are 63 coloring books packed equally in 9 boxes. How many books does each box have?
Answer:

Total number of coloring books = 63

Repeated subtraction method:

Long Division Method

63  -9 = 54

54 – 9 = 45

45 – 9 = 36

36 – 9 = 27

27 – 9 = 18

18 – 9 = 9

9 – 9 = 0 (there are seven equal sets of 9) Number of books each student got = 63 ÷ 9 = 7

NCERT Workbook Solutions For Class 3 Chapter 3 Multiplication And Division Combined operations

Question 1. Choose the correct alternative.

1. 50+5=10 also means

1. 5×10=50
2. 10+5=15
3. 50-10=40
4. 50+10=60

Answer: 1. 5 x 10 = 50

2. Vineet shared two dozen candies among his 6 friends. How much did each one get?

1. 12
2. 24
3. 4
4. 2

Answer: 3. 4

3. 48 saplings were arranged in rows of 6. How many saplings are there in each row?

1. 8
2. 7
3. 6
4. 4

Answer: 1. 8

4. There are 60 books arranged in 5 shelves. How many books are there on a shelf?

1. 6
2. 10
3. 16
4. 12

Answer: 2. 10

5. A vase can hold 3 flowers. If there are 21, flowers, how many vases do you need to hold the flowers?

1. 5
2. 7
3. 18
4. 12

Answer: 2. 7

2. Match the Column-1 with Column-2.

Answer. (1) → B, (2) → E, (3) → A, (4) → C, (5) → D

Question 3. State whether the following statements are True or False.

1. 3×3+3+3 ()
2. 14,21 and 37 are multiples of 7. ()
3. 2,4 and 8 are factors of 8. ()

Question 4. Fill in the blanks.

Question 5. Very Short Answer Type Questions.

1. 5 × 20 = 5 ×____ × 10 = ____

2. 4 × 40 = 4 ×____ × 10 =____

Answer:

1. 5 x 20 = 5 x 2 x 10 = 100

2. 4 x 40 = 4 x 4 x 10 = 160

Question 6. Activity Corner

Students of a class are required to do a bridge construction project, based on the following model.

They were divided into groups and each group was given the same number of sticks.

1. Number of blue sticks 5× _ = 30
2. Number of brown sticks 5×_ = 20
3. Number of green sticks 5× _ = 10
4. A total of 360 sticks were used by the class. How many groups were there?

Answer:

1. Number of blue sticks 5 x 6 = 30
2. Number of brown sticks 5 x 4 = 20
3. Number of green sticks 5 x 2 = 10
4.  6 groups

NCERT Workbook Solutions For Class 3 Chapter 5 Time, Calendar And Money

Concept Review Introduction

Time keeps changing continuously. lt refers to the past, present, and future. Time helps us to have an organized schedule in our life. A clock or a watch helps us to read time. We measure a point of time in hours, minutes and seconds.

• Similarly, Calendar is a visual tool used to organize days. Days are grouped together as month and year. When we represent a particular series of events, we use a timeline.
  Money is a medium of exchange for any product or service.
• We learn about the value of money and its calculation to help in paying and receiving money. Currency is a particular system of money used in a country or region.
• There are different currencies around the world that are used today. The official currency of lndia is the Rupee, whose lower denomination is the paisa.

Read and Learn More Class 3 Workbook Solutions

NCERT Workbook Solutions For Class 3 Time, Calendar And Money Time

The Clock

Clock is an instrument which helps us to read and measure time. There are two types of clocks – digital clock and analog clock. It is easy to read the time from a digital clock as the time appears as numbers. The analog clock has a different structure, which gives a particular time of the day.

Analog clock

• Analog clock has continuously moving hands which help us to read the time of the day.
• This clock is based on the following.
• A day has 24 hours, divided into two parts (12 + 12). 12 hours from midnight to afternoon, called the A.M. (anti-medium or before mid-day) and 12 hours from afternoon to midnight, called the P.M. (post meridium or after mid-day).

An Analog clock has the following markings.

1. The dial on which numbers are marked from t to 12, represents hours of the day. Each hour is divided into 5 equal divisions or minutes, to bring up 60 minutes.
2. A second’s hand is the thinnest and the fastest moving hand. When the second-hand makes one complete rotation, the time taken is 60 seconds or 1 minute.
3. A minute hand makes a complete rotation in 60 minutes or 1fThe hour hand is on lL and the minute hand is on 12. hour.
4. An hour hand is the shortest. lt makes two complete rotations of 12 hours in a day to complete 24 hours.

Telling Time From A Clock:

While reading the time from an analog clock, we must see the position of the hour hand and minute hand.

1. When the minute hand is on 12 and the hour hand is on any number, the hour of the day is the number on which you see the hour’s hand’.

Example 1.

Note: The minute hand and the hour hand, will point exactly at 12, only 2 times in a day at 12 A.M. (midnight) and 12 P.M. (Noon).

2. When the hour hand is in between two numbers, the lesser number is the hour of the day. The position of the minute hand indicates the minutes that have passed in a specific hour.

Example 2.

Question 1. Telling In Quarter And Half

• The minute hand of a clock completes one round in 60 minutes or 1 hour.
• Each 15 minutes is a quarter of an hour.
• 30 minutes is half of an hour (half of 60 minutes).

When the minute hand has moved one quarter of an hour or 15 minutes, we call it a quarter past.

The time on the clock is 5:15 or a quarter past 5.

When the minute hand has moved on half of an hour or 30 minutes, we call it half past.

The time in the clock is 7:30 or half past 7.

When the minute hand has moved a quarter of an hour or 45 minutes, we call it a quarter to.

The time in the clock is 2:45 or quarter to 3.

Question 2. 24-hour time

The time of the day in 24-hour format is written from 00:00 (12 midnight) to 23:59 The following table gives the hourly conversion.

Conversion Of Time (hours, minutes, and seconds)

We do time conversion based on the following rules:

1 day = 24 hours

1 hour = 60 minutes

1 minute = 50 seconds

Example 3. Convert 2 hours into minutes.

1 hour = 60 minutes

2 hours = 2 × 60 = 120 minutes

Example 4. Convert 20 minutes into seconds.

1 min = 50 seconds

20 min = 20 × 60 = 1200 seconds

Example 5. Convert 120 seconds into minutes

60 seconds= 1 minute

120 seconds = 120 ÷ 60 = 2 minutes

Example 6. Convert the A.M. and P.M. time to 24-hour time.

1. 7:30 A.M. = 07:30 hours
2. 5:00 P.M. = 5 + 12 = 17:00 hours

Example 7.

Convert the 24-hour clock to A.M. and P.M.

06:32 hours = 6:32 A.M.

14:20 hours =2:20 P.M. (As 14-12=2)

NCERT Workbook Solutions For Class 3 Time, Calendar And Money Time

Question 1. Choose the correct alternative.

1. Convert 10 minutes into seconds.

1. 600 sec
2. 60 sec
3. 6 sec
4. 10 sec

Answer: 1. 600 sec

2. Which of the following represents half past 12?

1. 11:30
2. 12:30
3. 1:30
4. 1:00

Answer: 2. 12:30

3. A dance recital was performed for 3 hrs. Estimate the time in minutes

1. 120 min
2. 30 min
3. 90 min
4. 180 min

Answer: 4. 180 min

4. A digital clock shows the time as 4:45. Tell the time in the quarter.

1. Quarter to 3
2. Quarter Past 3
3. Quarter to 5
4. Quarter Past 4

Answer: 3. Quarter to 5

5. The time at noon and midnight is represented by

1. 12 A.M., 12 P.M.
2. 12 P.M., 12 A.M
3. 12 A.M., 12 A.M.
4. 12 P.M.,12 P.M.

Answer: 2. 12 P.M., 12 A.M.

Question 2. Match the Column-1 with Column-2.

Answer. (1) → B, (2) → C, (3) → D, (4) → A

Question 3. State whether the following statements are True or False.

1. Quarter past 4 is the same as 3:35.
Answer: True

2. The school bell rang at 15:30, the time on my watch was 3:30 P.M.
Answer: True

Question 4. Fill in the blanks.

1. Riya works in her garden every day for t hour. If she starts at quarter to 4, the time in her digital clock is ___.
Answer: 3 : 30 P.M.

2. Tina’s mom finished cooking dinner in one hour and 15 minutes. The time taken by her is ___ minutes.
Answer: 75 minutes

NCERT Workbook Solutions For Class 3 Time, Calendar And Money Calendar And Timeline

Calendar

A calendar is an organized form of days and months.

A calendar year = 12 months

table

• Every month is divided into weeks of 7 days, which are Sunday, Monday, Tuesday Wednesday, Thursday, Friday, and Saturday.
• The number of weeks and number of days in the months are not the same.
• A normal year has 365 days. o A leap year has 366 days. The extra day is added in the month of February as 29 days.
• We write a particular day in the calendar as a date/month/year.

Example: August 15 is celebrated as India’s Independence Day. lt can also be written as 15/08/2022. We can see from the calendar that day is a Monday.

Example 1. What date is the first Friday of April 2022?
Answer: 01/04/2022

Example 2. Ria’s birthday falls on 7th March and her brothel Ravi’s birthday is two months later the same date. When is Ravi’s birthday?
Answer: Two months after March is the month of May.

Ravi’s birthday is on 07/05/22.

Timeline

A timeline is used to show the happening of a particular event and when it happened. The order of the events from past to future can be shown either from left to right or from top to bottom.

This is a timeline about Reshma.

• She was born in 2009.
• Reshma joined play school when she was 3 years old.
• She joined her first tennis class after 6 years in school.
• Two years later she got her pet dog and its second birthday will be in 2022.

Estimating time

Time taken for an activity will be different for people depending on how fast or slow they do it. We can estimate time required for certain activities by experience, observation or logic.

Task which can be done in few seconds

Ring a bell, sit down, stand up, water a plant, wearing socks and so on.

Task which needs few minutes

Washing the hands, filling water in a bottle, packing your bag and so on.

Task which needs an hour or more

Watching a movie, making lunch, cleaning the cupboard and so on.

Elapsed Time

Elapsed time is the exact time when you started an activity and when you finished it. A clock is very helpful in calculating elapsed time. We can also use a number line to help calculate elapsed time.

Example 3.

The dance class started at 4:00 P.M. and got over at 5:30 P.M. We can use mental maths and calculate the elapsed time as 1 hour and 30 minutes. We can also use a number line to find the elapsed time.

• Start time = 4:00 pm
• End time = 5:30 pm
• Draw a number with hours and minutes as shown.
• The elapsed time is t hr and 30 min.

NCERT Workbook Solutions For Class 3 Time, Calendar And Money Calendar and Timeline

Question 1. Choose the correct alternative.

1. The number of months in a calendar year are

1. 10
2. 12
3. 24
4. 365

Answer: 2. 12

2. The number of days in a leap year are

1. 364
2. 365
3. 366
4. 368

Answer: 3. 366

3. A knitting course was organized for 3 weeks. How many days was the course for?

1. 21
2. 20
3. 14
4. 30

Answer: 1. 21

4. Train service to a particular station is on every third day. If the train comes on Tuesday, when will it come to the station next?

1. Saturday
2. Tuesday
3. Today
4. Friday

Answer: 3. Today

5. Aryan was born on the 8th month of 2007. The month is

1. August
2. July
3. September
4. December

Answer: 1. August

Question 2. Match the Column-1 with Column-2.

(observe the given calendar)

Question 3. State whether the following statements are True or False.

1. There are only 30 days in a month
Answer: False

2. Every month has 5 weeks.
Answer: False

Question 4. Fill in the blanks.

(Identify the facts from the given timeline)

First telephone existed in the year ___. In 1920 was ___ the model of telephone commonly used. The cordless phone used during _ enabled us to move with the phone in a small area. ___ was the year when the mobile phone came into use. The ___ which we use today are there from the year 2011.

Answer:

First telephone existed in the year 1876. In 1920 was Phone Box the model of telephone commonly used. The cordless phone used during 1970s enabled us to move with the phone in a small area. 1990 was the year when the mobile phone came into use. The Smartphone which we use today are there from the year 2011.

Question 5. Very Short Answers Type Questions.

1. How many days does a leap year have?
Answer: 366 days

2. What are the 2nd and 5th months of the Gregorian calendar?
Answer: February, May

3. If a month ends on a Tuesday, on what day does the next month begin?
Answer: Wednesday

NCERT Workbook Solutions For Class 3 Time, Calendar And Money Money

We buy or sell anything by exchanging a certain amount of money. Money is usually in the form of paper notes or coins, issued by a government. They have a specific standard of design and size.

If I have 5 notes of ₹20 denomination and 2 notes of ₹100 denomination, what is the value of money I have?

5 notes of ₹ 20 = 5 × 20 = ₹100

2 notes of  ₹100 =2 × 100 = ₹200

So, ₹100+₹200= ₹300

Currency And Denomination

Money is the common word used for currency. The six most popular currencies of the world are:

1. The American dollar ($)
2. The Euro (€)
3. The Canadian Dollar (C$)
4. The British Pound (£)
5. The Japanese Yen (¥)
6. The Swiss Franc (₣)

The currency which we use in India is the Rupee (symbol: ₹ code: INR).

• Splitting currency into smaller currencies is called denomination.
• Each rupee is divided into a denomination of 100 paise.
• Till 2019, we had paisa of denominations like 10 paisa, 20 paisa, 25 paisa and 50 paisa. Currently, ₹ 1 is the lowest denomination in use.

The denominations of rupee notes in circulation are ₹ 5, ₹10, ₹ 20, ₹ 50, ₹ 100, ₹ 200, ₹ 500, ₹ 2000

Conversion Of Rupees And Paise

When we use money, we need to give or take a specific value. For this, we need to know the denomination.

ln the Indian Rupee

1 rupee = ₹ 1=100 paise

It is also written as ₹ 1.00.

Converting Rupees To Paise

Follow the below steps to convert the rupee into paisa.

Convert the rupee to paisa by multiplying it with 100.

Add it to the given paise.

Example 1. Convert ₹ 5 to paise.

₹ 1 = 100 paisa

₹ 5 =5 × 100 = 500 paisa

Example 2. Convert ₹ 6.75 to paise

₹1= 100 paise

₹ 6.75 = 6.75 × 100 = 675 paise

Converting Paise To Rupees

Follow the below steps to convert paise to rupees Convert the paise to rupees by dividing by 100.

Example 3. Convert 455 paise to rupees.

1, 1p= ₹ \(\frac{1}{100}\).

455p=455÷100= ₹4.55

Example 4. Convert 7570 paise to rupees.

1p= ₹ \(\frac{1}{100}\)

7570 p = 7570 ÷ 100 = ₹ 75.70

Operations

Addition:

₹ 25.30 and ₹ 30.70

₹ 25.30+ ₹30.70= ₹56.00

Subtraction:

₹ 100.50 and ₹ 60.50

₹ 100.50 – ₹ 60.50 = ₹ 40.00

NCERT Workbook Solutions For Class 3 Time, Calendar And Money Money

Question 1. Choose the correct alternative.

1. The currency of India is

1. Coin
2. Rupee
3. Paisa
4. Dollar

Answer: 2. Rupee

2. Rupee six hundred and seventy-five paise is written as

1. 600.75
2. 60075
3. 60.75
4. 6750

Answer: 1. 600.75

3. Hundred ten rupee is same as

1. ₹ 100
2. ₹ 500
3. ₹ 1000
4. ₹ 10000

Answer: 1. ₹ 100

4. Ravi had 4000 paise in his piggy bank. The amount in rupee he has is?

1. ₹ 4000
2. ₹ 400
3. ₹ 4
4. ₹ 40

Answer: 1. ₹ 4000

5. The cost of a pack of pencils is t 60. If sanya gave 100 to the shopkeeper, how much money will she get back?

1. ₹ 40
2. ₹ 20
3. ₹ 30
4. ₹ 10

Answer: 1. ₹ 40

Question 6. 50 students of class 3 contributed ₹ 2,000 for the Diwali party. If every student contributes equally then how much money is collected at the end?

1. ₹ 40
2. ₹ 200
3. ₹ 10
4. ₹ 500

Answer: 1. ₹ 40

Question 2. Match the Column-1 with Column-2.

Answer. (1) → D, (2) → E, (3) → B, (4) → C, (5) → A

Question 3. State whether the following statements are True or False.

1. Currency and money are not the same
Answer: False

2. Twenty ₹ 5 coins make ₹ 100.
Answer: True

Question 4. Very Short Answer Type Questions.

1. Calculate the total amount of three chairs and two tables, if the cost of one chair and one table are ₹ 230 and ₹ 300 respectively.
Answer: ₹ 1290

2. Madan has ₹ 500 to buy a hat. The cost of the hat is ₹125. How many hats can he buy?
Answer: 4 hats

Question 6. Short Answer Type Questions.

1. Observe the following rate list:

Find the cost of 1 plate of fried rice, 1- a plate of butter paneer, and 1- a cup of coffee.

Answer. 1 plate of fried rice = 230

1 plate of butter paneer = 175

1 cup of coffee = 25

∴ ₹ 230 + ₹ 175 + ₹ 25 = ₹ 430

NCERT Workbook Solutions For Class 3 Chapter 7 Fractions

Concept Review Introduction

Fraction means a part of a whole. Fraction represents equal parts of a whole or a collection.

• A fraction has a numerator denominator and a fraction bar. We can represent fractions in numbers, figures and a number line.
• We can compare fractions with same denominator. We can add and subtract Like Fractions To Get Their Sum Or Difference.
• There are six types of fractions – proper, Improper, mixed, like, unlike and equivalent.

Read and Learn More Class 3 Workbook Solutions

NCERT Workbook Solutions For Class 3 – What are Fractions?

When We Divide A Whole Thing Into Equal Parts, We Represent The Parts Using Fraction. Consider The Following:

Parts of a fraction:

Representation Of Fractions:

Fractions can be represented in numbers, figures and on a number-line.

Simple Form Of Fractions:

To express the fraction in its simplest or lowest form, we divide numerator and denominator by the common prime factor till no more common prime factor is able to divide further.

Example 1. \(\frac{18}{54}\) 

Answer:

⇒ \(\frac{18 \div 2}{54 \div 2}=\frac{9}{27}\)  [Here, common Prime factor is 2.]

⇒ \(\frac{9 \div 3}{27 \div 3}=\frac{3}{9}\)  [Here, common Prime factor is 3.]

⇒ \(\frac{3 \div 3}{9 \div 3}=\frac{1}{3}\) The Simple From of \(\frac{18}{54} \text { is } \frac{1}{3}\)

NCERT Workbook Solutions For Class 3 What are Fractions?

Question 1. Choose The Correct Alternative.

1. What fraction of even numbers is there in the first twenty natural numbers?

1. \(\frac{1}{20}\)
2. \(\frac{11}{20}\)
3. \(\frac{10}{20}\)
4. \(\frac{12}{20}\)

Answer: 1. \(\frac{1}{20}\)

2. ln the given figure, what is the fraction of blue shapes?

1. \(\frac{3}{5}\)
2. \(\frac{2}{5}\)
3. \(\frac{3}{3}\)
4. \(\frac{5}{5}\)

Answer: 1. \(\frac{3}{5}\)

3. If there are a dozen mangoes in a basket and five are ripe, what is the fraction of unripe mangoes?

1. \(\frac{5}{12}\)
2. \(\frac{7}{12}\)
3. \(\frac{5}{7}\)
4. \(\frac{7}{5}\)

Answer: 1. \(\frac{5}{12}\)

4. The temperature of a place for one week is recorded as follows. What is the fraction of sunny days?

1. \(\frac{1}{7}\)
2. \(\frac{2}{7}\)
3. \(\frac{3}{7}\)
4. \(\frac{4}{7}\)

Answer: 2. \(\frac{2}{7}\)

5. ln the given figure, the fraction of coloured portion in the circle

1. \(\frac{10}{12}\)
2. \(\frac{2}{12}\)
3. \(\frac{8}{12}\)
4. \(\frac{12}{12}\)

Answer: 1. \(\frac{10}{12}\)

Question 2.  Match the Column-1 with Column-2.

Answer: (1) → B, (2) → E, (3) → F, (4) → C, (5) → A

Question 3.  Fill in the blanks

1. Whole number 7 when written as fraction is ____________
Answer: \(\frac{1}{7}\)

2. In a word EXPAND, the fraction of consonants is_________
Answer: \(\frac{2}{6}\)

Question 4.  State whether the following statements are true or false

1. Simplest form of a fraction \(\frac{125}{500} \text { is } \frac{5}{8}[latex]
Answer: False

2. ln a fraction, the denominator represents the number of divisions of the whole.
Answer: True

Question 5.  Very Short Answer Type Questions.

1.  Mom gave me 12 muffins and I gave 6 to my sister. What is the remaining fraction of muffins with me?
Answer: [latex]\frac{6}{12}\)

Question 6.  Short Answer Type Questions.

1. In a class of 25,7 children use the school bus and the remaining use private transport. This can be represented in fraction as

1. Children who use school bus = 7 children
2. Children who use private transport = 18

Answer: \(\frac{7}{18}\)

2. Simplify the following:

Answer: 

1. \(\frac{152}{8} \times 5+27-10\)

= 19 x 5 + 27 – 10

= 19 x 5 + 17

= 95 + 17

= 112

2. \(\frac{100}{6} \times 9+\frac{23}{2} \times 10-10\)

= 16.7 x 9 + 11.5 x 10 – 10

= 150.3 + 115 – 10

= 150.3 + 105

= 255.3

3. ln the figure given below find the fraction of shaded parts of the whole figure.

Answer:

1. \(\frac{4}{8}\) = \(\frac{1}{2}\)

2. \(\frac{1}{4}\)

3. \(\frac{1}{4}\)

4. \(\frac{5}{5}\) = 1

Question 7.  Long Answer Type Questions:

Answer the following question by observing the calendar.

1. what is the fraction of holidays in the month, including Saturday and Sunday?
Answer: \(\frac{8}{31}\)

2. Divya has music classes on Mondays and Thursdays. What fraction of the month does it represent?
Answer: \(\frac{9}{1}\)

3. If there are 52 weeks in the whole year, what fraction of weeks are in December?
Answer: \(\frac{4}{52}\)

Question 8.  Activity Corner

Fill in the chart, whisper the total number of fractional units.

Types Of Fractions And Operations

There are six types of fractions on the basis of numerator and denominator value such as proper, improper; mixed, like, unlike and equivalent. Fraction can be converted from one type to another. We can add and subtract like fractions to get their sum or difference.

Proper Fraction

A fraction in which the numerator is less than the denominator is called a proper fraction

Example 1.

2/5, two parts of five shaded parts (2<5)

\(\frac{3}{5}\), three parts of five shaded parts (3<5)

Improper fraction

A fraction in which the numerator is greater than the denominator is called an improper fraction

Example 2.

⇒ \(\frac{8}{5}\) Eight Shaded Parts Of Two Whole, Divided Into Five Equal Parts. (8>5)

⇒ \(\frac{5}{4}\), five shaded parts of two whole, divided into four equal parts. (5>4)

Mixed Fraction

A fraction in which there is a whole number along with the numerator and denominator is called a mixed fraction.

• The value of a mixed fraction is always greater than 1.
• Mixed fractions have a whole number and proper fraction.
• Improper fractions can be converted into mixed fractions.

⇒ \(1+\frac{1}{4}=1 \frac{1}{4}\)

This fraction represents \(\frac{5}{4}\) which is same as 1 \(\frac{1}{4}\)

Example: Convert \(\frac{7}{5}\) into mixed fraction.

Example: Convert \(\) into improve fraction.

Answer:

Like Fraction

Fractions which have the same denominator are called like fractions

⇒ \(\frac{2}{8}, \frac{5}{8}, \frac{7}{8}\) are examples of like fractions

Unlike Fraction

Fractions which have different denominators are called unlike fractions

⇒ \(\frac{12}{9}, \frac{25}{20}, \frac{18}{12}, \frac{100}{70}\)  are examples, of unlike fractions

Equivalent Fraction

When two or more fractions represent the same value and can be simplified to the same numerator and denominator are called equivalent fractions.

⇒ \(\frac{1}{2}\)

⇒ \(\frac{3}{6}\)

Both the functions \(\frac{1}{2} \text { and } \frac{3}{6}\) are half of a Whole

Equivalent Fractions

We can find equivalent fraction by method of multiplication or division. For this the numerator and denominator should be multiplied (or divided) by a non-zero number

Example. Find 3 equivalent factions of \(\frac{2}{5}\)

Answer: \(\frac{2}{5} \times \frac{5}{5}=\frac{10}{25} \times \frac{5}{5}=\frac{50}{125} \times \frac{5}{5}=\frac{250}{625}\)

The 3 equations factors of \(\frac{2}{5} \text { are } \frac{10}{25}, \frac{50}{125} \text { and } \frac{250}{625}\)

Example 1. Find two equivalent factors of \(\frac{40}{72}\)

Answer: \(\frac{40 \div 2}{72 \div 2}=\frac{20 \div 4}{36 \div 4}=\frac{5}{9}\)

The two-equivalent factors of \(\frac{40}{72} \text { are } \frac{20}{36} \text { and } \frac{5}{9}\)

Comparing fractions

We can compare two fractions when they have the same denominator. A fraction with the greater numerator will represent the larger value.

Example 2. Compare \(\frac{3}{7} \text { and } \frac{5}{7}\)

Answer: 

Example 3.  Compare\(\frac{13}{15}, \frac{11}{15} \text { and } \frac{9}{15}\)

Answer:  \(\frac{9}{15}<\frac{11}{15}<\frac{13}{15}\)

Adding fractions

To add two or more like fractions, add the values in the numerator and keep the denominator same.

Example 1.  Add \(\frac{5}{9} \text { and } \frac{3}{9}\)

Answer: \(\frac{5}{9}+\frac{3}{9}=\frac{5+3}{9}=\frac{8}{9}\)

Subtracting fractions

To subtract two or more like fractions, subtract the lesser value from the greater value in the numerator and keep the denominator same.

Example 1.  Subtract \(\frac{50}{60} \text { and } \frac{25}{60}\)

Answer:  \(\frac{50}{60}-\frac{25}{60}=\frac{50-25}{60}=\frac{25}{60}\)

NCERT Workbook Solutions For Class 3 Fractions Types of Fractions and Operations

Question 1.  Choose the correct alternative

1. Identify the like fractions

1. \(\frac{7}{52}, \frac{7}{53}\)
2. \(\frac{17}{71}, \frac{71}{17}\)
3. \(\frac{7}{53}\)
4. \(\frac{7}{53}, \frac{51}{53}\)

Answer: 4. \(\frac{7}{53}, \frac{51}{53}\)

2. \(1\frac{5}{7}\) can also be written as

1. \(\frac{1}{7}\)
2. \(\frac{12}{7}\)
3. \(\frac{5}{7}\)
4. \(\frac{35}{7}\)

Answer: 2. \(\frac{12}{7}\)

3.  can be Written as

1. \(\frac{10}{3}\)
2. \(\frac{1}{3}\)
3. \(\frac{9}{3}\)
4. \(\frac{11}{3}\)

Answer: 1. \(\frac{10}{3}\)

4. The equivalent fraction of is

1. \(\frac{4}{6}\)
2. \(\frac{1}{2}\)
3. \(\frac{2}{4}\)
4. \(\frac{8}{12}\)

Answer: 1. \(\frac{4}{6}\)

5. There are 27 students in a class and 17 of them are girls. The fraction of boys

1. \(\frac{27}{17}\)
2. \(\frac{27}{10}\)
3. \(\frac{10}{27}\)
4. \(\frac{17}{27}\)

Answer: 3. \(\frac{10}{27}\)

Question 2.  State whether the following statements are true or false.

1. \(\frac{7}{14} \text { and } \frac{1}{3}\) are like fraction

Answer: False

2. \(\frac{100}{200}+\frac{20}{200}=\frac{120}{400}\)

Answer: False

Question 3. Fill in the blanks

1.

Answer: \(\frac{4}{10}\), \(\frac{6}{10}\), \(\frac{8}{10}\)

2.

Answer: \(\frac{2}{10}\), \(\frac{6}{10}\)

Question 4.  Very Short Answer Type Question

1. There are 12 apples, 10 mangoes and 6 guavas in a basket.

1. What fraction of the fruits is apples?
2. What fraction of fruits is not a guava?

Answer:

1. \(\frac{12}{28}\)

2. \(\frac{22}{28}\)

Question 5. Activity Corner

The following is a table of different books in the school library. The total number of books available in the library are 200.

represents 5 books

1. What is the fraction of magazines available in the library?
Answer: \(\frac{15}{70}\)

2. What fraction of English books have been issued to the students?
Answer: \(\frac{20}{80}\) = \(\frac{1}{4}\)

3. Compare the fraction of books issued to the students with those available in the library.  Which is greater?
Answer: Issued to students

NCERT Workbook Solutions For Class 3 Chapter 6 Geometry

Concept Review Introduction

Geometry is a branch of mathematics that deals with properties and measurements of different points, lines, shapes, angles, etc. Geometry Is derived from two ancient Greek words, ego – earth” and melton – “measurement”.

• In euclidean geometry, there are two-dimensional (2 d) and three-dimensional (3 d) shapes. angle is a measurement formed when two lines or rays meet at a point.
• We study different shapes in geometry such as triangle, squares are all polygons. polygons are closed figures formed from Joining line segments.
• we see different tessellations, tangrams around us where geometry is applied.

Read and Learn More Class 3 Workbook Solutions

Basic Concepts Of Geometry

A shapes the form of an object, its outline or border. shapes are made of points, lines, curves, angles, and plane surfaces. the general terms used in geometry shapes are as follows.

Curve

When a line is smooth flowing and does not have any sharp turns, it is called a curve.

Curve Example: The outline of the ceiling fan, The transparent Glass Of The Washing Machine.

Curves that Join to form an enclosed Area Are called closed curves And curves That Do not Intersect are called open curves

Angles

The Inclination between two rays is called an Angle. In geometry, an Angle Is The Measurement between Two Rays Meeting At A Point, Called a Vertex. The Two Rays Are Called The Arms of the angle. we use a tool called Protractor To Measure Angles.

• The Arms Meet At Vertex.
• The Unit Of Angle Is Degrees.

As The Arms Turn, The Angle Changes

We Can See Angles In Real Life From The Flip Of A Page To The Construction Of A Building. Types Of Angles Can Be Easily Understood By Observing The Hands Of A Clock.

Types Of Angles

1. Acute angle Is less than 90°.
2. Right angle Is equal To 90°.
3. Obtuse angle Is more than 90°.
4. Straight angle Is Equal To 180°.
5. Reflex angle Is greater Than 180′ but less than 360°.
6. The complete angle Is equal to 360°

NCERT Workbook Solutions For Class 3 Basics Concepts Of Geometry

Question 1. Choose The Correct Alternative.

1. Which Of The Following Is A Ray?

1. Book Outline
2. A Stick
3. Sun Light
4. A Rope

Answer: 3. Sun Light

2. Identify The Line Segments In the given figure

1. \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CD}} \text { and } \overline{\mathrm{AD}}\)
2. \(\overline{\mathrm{AD}} \text { and } \overline{\mathrm{AB}}\)
3. \(\overline{\mathrm{AD}} \text { and } \overline{\mathrm{CD}}\)
4. \(\overline{\mathrm{AB}} \text { and } \overline{\mathrm{CD}}\)

Answer: 1. \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CD}} \text { and } \overline{\mathrm{AD}}\)\

3. Which Of The Following Alphabets Have Perpendicular Lines

1. A
2. M
3. H
4. R

Answer: 3. H

4. How Many Sets Of parallel lines are there In the Outline Of a television Screen

1. 1
2. 4
3. 2
4. 3

Answer: 2. 4

5. Which Of The Following Is A Straight Line?

Answer: 2. Straight line

6. Which Of The Figures Represent Intersecting Lines?

Answer: 3. Intersecting lines

Question 2. Match The Column-1 With Column-2.

Answer. (1) → C, (2) → A, (3) → B

Question 3. State Whether The Following Statements Are True Or False.

1. An angle measure of 180° is called a straight angle.
Answer: True

2. The surface of earth Is covered with Infinite points.
Answer: False

3. A-Line does not have a fixed length.
Answer: False

4. any two perpendicular Lines can be Intersecting lines but their reverse Is not true.
Answer: True

Question 5. Short Answer Type Questions.

1. What Is The Angle formed between the hands of a clock when the time Is 9 O’clock?
Answer: Right Angle

NCERT Workbook Solutions For Class 3 Shapes 2d And 3d

• Flat shapes are called 2d shapes or two-dimensional shapes
• Solid objects are 3d shapes or three-dimensional objects.

2d Shapes

Figures that can be drawn on a Plane or paper are called two dimensional Or 2d Shapes. they have only Length and breadth. they do not have Any thickness such that 2d shapes can have sides and corners or curved boundaries.

2d Shapes which Are closed and Have straight sides are called polygons. poly means ‘many’ and Gon means ‘sides’.

Polygons Of different sides and their names

3d Shapes

Solids Or 3d shapes as the name suggests have three dimensions – length, breadth, and height. they can be either hollow or solid. 3d shapes can have either a flat surface or a curved surface.

we use the following terms to define a 3d shape – faces, edges, and vertices.

NCERT Workbook Solutions For Class 3 Shapes 2d And 3d

Question 1. Choose The Correct Alternative.

1. The cube And cuboid have an equal number of _______

1. Faces and vertices
2. Faces and vertices
3. Faces
4. Vertices

Answer: 3. Faces

2. Which of these statements does not define a circle?

1. A circle is A Polygon.
2. A circle is A closed curve
3. A circle has Radius
4. A circle has one Centre

Answer: 2. A circle is a Polygon.

3. Which Of these options is not a quadrilateral?

1. Square □
2. Rectangle ▭
3. Triangle △
4. Kite ⟡

Answer: 3. Triangle

4. How many squares are there in the given rectangle?

1. 1
2. 4
3. 2
4. 3

Answer: 4. 3

5. How many triangles are there in this figure?

1. 8
2. 3
3. 6
4. 5

Answer: 2. 3

6. How many vertices does a sphere have?

1. 0
2. 1
3. 2
4. 3

Answer: 1. 0

Question 2. match the column-1 with column-2

Answer. (1) → E, (2) → A, (3) → D, (4) → C, (5) → B

Question 3. State Whether The Following Statements Are True Or False

1. A Hollow cylinder is formed when you roll a paper along a side
Answer: True

2. A cube has 8 Squares As Its Faces.
Answer: False

3. There are 3 edges in a cone
Answer: False

Question 7. Activity Corners

Observe the figure and answer the following.

Number Of Circles = 5

Number Of Triangles = 16

Difference Between Triangles And Circles = 16 – 5 = 11

NCERT Workbook Solutions For Class 3 Application Of Geometry

Polygons have various applications in our life. They are paper folding or the art of Origami, tangrams, tessellations and map reading.

Paper folding or the art of origami

Origami Is the art of paper folding Associated with the Japanese culture. with this method, It Is possible to create different shapes from a single piece of paper, without cutting. construction through paper folding Is both mathematically Interesting and pleasing to look at

Origami Sailboat

Tangrams

A Tangram Has 7 Geometric shaped sheets or blocks: 5 triangles, 1 square And 1 parallelogram. these 7 shapes can be Arranged In Different ways to form different shapes or figures.

Rules of a tangram puzzle.

Rule 1: All 7 Pieces Should Be Used.

Rule 2: No Piece Should Overlap.

Rule 3: Each Piece Should Touch One Another.

Benefits of tangram: It Helps Us To Understand spatial relationships and problem solving skills.

Some Tangram Puzzle Solutions

Tessellation

Tessellation or tiling Is covering a given plane with shapes and without any overlap or gaps.

Regular Tessellation

Regular tessellations are created with regular polygons (Polygons whose all sides are equal In length). there are only three regular tessellations: those made up of equilateral triangles, squares or regular hexagons.

The honey comb Is a well-known example of tessellation in nature with Its hexagonal cells.

Map Reading

• A map Is A Flat drawing which helps us to know the details of a place and Directions.
• The basic components of a map are compass, title, legend or key and symbols.
• A grid enables us to say the exact location of a particular symbol.

Example:

Title: It Indicates the purpose of the theme of the map. example-world, India, political, etc. given here is a simple map of a town.

Compass: It shows the directions east, west, north and south using the compass, we can say that the school is in the western side of the railroad and the restaurant Is to the east of the railroad.

Legend or key: It gives the list of symbols used In the map symbols: symbols are figures used to represent real life structures.

Application Of Geometry

Question 1. Choose The Correct Alternative.

1. Identify the number of triangles seen in the origami swan.

1. 4
2. 5
3. 6
4. None

Answer: 2. 6

2. The number of quadrilaterals in a tangram puzzle are

1. 7
2. 5
3. 4
4. 2

Answer: 2. 5

3. Identify the number of sides of the polygon in the middle of the tessellation

1. 10
2. 11
3. 12
4. 13

Answer: 4. 13

5. The polygon which forms this tessellation with its mirror image is

1. Hexagon
2. Pentagon
3. Heptagon
4. Octagon

Answer: 1. Hexagon

Question 2. Match The Column-1 With Column-2.

Match the columns and select the correct option

Answer. (1) → C, (2) → A, (3) → B

Question 3. State Whether The Following Statements Are True Or False.

1. There are five squares in a tangram puzzle.
Answer: False

2. The symbols in a map represent real life structures
Answer: True

Question 4. Fill In The Blanks.

(Use The map and key to complete the following)

1. The _________ is in D4 and the bus stop is in______
Answer: The Book is in D4 and the bus stop is in B2

2. ________ is in C5 and _____ is to the west of bus stop
Answer: School is in C5 and D5 is to the west of bus stop

NCERT Workbook Solutions For Class 3 Chapter 8 Chapter 8 Data Handling

Concept Review Introduction

Any Data Is Collected Based On The Information. Data Collection Involves Collecting Data, Organizing, Or Tabulating Data And Data Representation. There Are Many Ways To Arrange Data In Pictograph, Bar Graph, Etc.

• Interpreting Data From Pictorial Representation Helps In Understanding Information. Pictograph Represents Numbers In The Form Of Pictures.
• They Are Used To Compare Data. Pictographs Are Often Used In Newspapers And Magazines. Bar Graph Uses Vertical Or Horizontal Bars To Represent Data.

Read and Learn More Class 3 Workbook Solutions

NCERT Workbook Solutions For Class 3 Chapter 8 Data Handling Data Collection And Organisation

Data

Data is A Collection Of Information. It is Gathered On The Basis Of Requirements. There Are Different Methods Of Collecting Data Such As By Observation, By Asking questions, or through measurements. the information can be represented in the form of the following:

• Facts: Vegetables grown in a particular region.
• Numbers: Marks of students in an exam.
• Measurements: Height of mountains of the world

Collection and Tabulation of Data

Data can be collected from different sources.

The Following Data Was Collected By A Group Of Students For A School Project. They Asked 30 People About Their Favourite Sport And Organized The Data.

We Use Tally Marking For Counting The Numbers. Lt Is A Representation Of Set Of Five Lines.

Every line | represents the number 1 and every fifth line is a diagonal line that represent number.

NCERT Workbook Solutions For Class 3 Chapter 8 Data Handling Data Collection And Organisation

Question 1. Choose the correct alternative

1. Identify the number represented by the tally mark

1. 11
2. 21
3. 13
4. 9

Answer: 1. 11

2. The number of triangles in the shape will be represented in tally mark as

Answer: 3.

3. The marks scored by a student in his test was identify the number

1. 37
2. 32
3. 42
4. 17

Answer: 4. 17

Study The Table That Represents The Number Of Medals Won By Kids In The Sports Organized In The School Premises.

Organizing And Tabulating The Collected Data, Makes It Easy For Us To Understand The Information

5. Difference between medals won by Rajan and Rahul in tally marks

Answer: 3.

6. are the medals won by _____

1. Rajshri
2. Pradeep
3. Poonam
4. Rajan

Answer: 3. Poonam

Question 2.  Match the Column-1 with Column-2

1. Match the columns and select the correct option.

represents 10 numbers and represents 5 numbers.

1. 1 → (D), 2 → (A), 3 → (B), 4 → (E), 5 → (C)
2. 1 → (C), 2 → (E), 3 → (A), 4 → (B), 5 → (D)
3. 1 → (E), 2 → (A), 3 → (D), 4 → (B), 5 → (C)
4. 1 → (B), 2 → (D), 3 → (A), 4 → (E), 5 → (C)

Answer: 1 → (D), 2 → (A), 3 → (B), 4 → (E), 5 → (C)

Question 3. State Whether The Following Statements Are True Or False.

Observe The Pictograph And Answer The Questions.

A Baker Recorded The Number of Customers Who Came To His Shop In A Particular Week.

1. The total customers who did not make any purchase in the week is

Answer: False

2. Number of people who purchased on Monday and Thursday are same as
Answer: True

3. Number of people who purchased on Wednesday, in tally mark is
Answer: False

4. Number of people who did not make any purchase on Tuesday is similar to the people who purchased on Friday.
Answer: True

Question 4. Activity Corner

The students in class recorded the lengths of their shoes to the nearest centimetre and make a tally chart. How many more shoes were 18 and 22 centimetres long combined than 20 centimetres long?

NCERT Workbook Solutions For Class 3 Chapter 8 Data Handling Representing Data: Pictograph And Bar graph

Pictograph

A pictograph is used to convey information of data using pictures and symbols. There are 4 details in a pictograph, the title of the data, label, symbol and key.

Title: Favourite game among 30 people

Here the label is the name of games and symbol is the circle.

Bar Graph

A bar graph uses bars to compare and represent data of a given information. Given below is the bar graph for the data collected by the students, to understand the favourite game among 30 people. The length of the bars represent the number of people.

From the above table we can answer the questions like,

• Which is the most popular game liked by the group – Cricket
• Which is the game of least preferred by the group – Tennis

Interpreting Pictograph

Example:

Number of books sold in a shop in a particular week.

1. How many books in total we sold in the week?
2. ln which days were least and most books sold?

Answer:

1. Total number of books sold = 15 × 5 = 75 Books
2. No book was sold on Friday and a maximum of 5 × 5 = 25 books were sold on Saturday.

Interpreting Bar Graph

Example.

A data is collected for the fruits preferred by students of a class.

1. Which is the fruit preferred by most of the kids?
2. How many kids preferred banana?
3. How many kids liked apple?

Answer:

1. Oranges = 6
2. Banana = 2
3. Apple = 4

Points to remember for handling data

• Understand the need for collecting a particular data.
• Read the data carefully.
• Organize the collected data in a table.
• Carefully analyze and interpret the data.
• pictographs and bargraphs can be done only with the help of tabulated data.
• Use a pictograph to represent small data and a bar graph to represent large data.
• Understand and interpret pictographs and bar graphs correctly using the keys.
• Organized data helps us to,
• Answer relevant questions
• Evaluate outcomes and
• Make predictions about future trends.

NCERT Workbook Solutions For Class 3 Chapter 8 Data Handling Representing Data: Pictograph And Bar Graph

Question 1.  Choose the correct alternative.

1. If each represents 2 players, identify the number of players given by

1. 3
2. 13
3. 6
4. 12

Answer: 4. 12

2. The score of 10 students in a test is recorded as 77, 100, 54, 92, 100, 63, 99, 100, 54,70. Number of students who got the highest and lowest scores are

1. 3,2
2. 2,3
3. 1,3
4. 3,1

Answer: 1. 3, 2

3. If each  stands for 10 trees. How many trees are there in the mango and orange orchard?

1. 8,5
2. 80,50
3. 40,25
4. 16, 10

Answer: 2. 80, 50

Observe the following pictograph and answer the questions 4 and 5.

Key :  = 3 girls and = 3 boys

4. Number Of Girls And Boys Having Birthday In The Whole Quarter (One Quarter Of A Year Is 3 Months)

1. 6,3
2. 12,6
3. 24,12
4. 18 and 9

Answer: 1. 6, 3

5. ln which month does the maximum number of boys have birthday?

1. March
2. February
3. January
4. January and February

Answer: 1. March

Question 2. Match the Column-1 with Column-2

Match the following columns and select the correct option.

1. 1 → (D), 2 → (C),3 → (A), 4 → (B)
2. 1 → (B), 2 → (D), 3 → (A), 4 → (C)
3. 1 → (D), 2 → (A), 3 → (C),4 → (B)
4. 1 → (B), 2 → (D), 3 → (A), 4 → (C)

Answer: 4. 1 → (B), 2 → (D), 3 → (A), 4 → (C)

Question 3. State whether the following statements are true or false

Directions: Observe the bar graph that depicts information about colour preferences of people.

1. Orange and indigo are the least preferred colours. 
Answer: True

2. Difference between the number of people who preferred steel and indigo is 6.
Answer: False

3. The number of people who preferred indigo and steel are 8 and 12 respectively
Answer: True

4. A maximum of 12 people preferred the colour ‘sunny’.
Answer: False

5. Total number of people who participated in the survey were 42.
Answer: False

Question 4. Very Short Answer Type Questions.

Directions: Study the bar graph that shows variations in the lowest temperature in January in different years.

1. How many years are recorded in the graph?
Answer: 10 years are recorded in the graph

2. Which year the lowest temperature was 18°?
Answer: 2019 year the lowest temperature was 18°

3. Which year had the day with lowest temperature in the month of January and at what date?
Answer: 2013 year had the day with lowest temperature in the month of January and at 3rd.

Directions: Study the pictograph that shows the number of cars Mr. James repaired last week

Key represents 6 cars.

4.

1. How many cars did Mr. James repair on Monday?
2. On which day the maximum number of cars were repaired?

Answer:

1. Mr. James 18 cars repair on Monday

2. The maximum number of cars were repaired on Thursday

5.

1. Did he repair 30 cars on Wednesday ?
2. On which day Mr. James didn’t do any work?

Answer: 

1. Mr. James doesn’t repair 30 cars on Wednesday.

2. Mr. James didn’t work on Sunday

6.

1. How many cars did he repair on Friday and Saturday?
2. How much more cars did he repair on Thursday than Wednesday?

Answer:

1. Mr. James 48 cars repair on Friday and Saturday

2. Mr. James 30 cars repair on Thursday than Wednesday

Question 5. Short Answer Type Questions.

Directions: Study the given pictograph showing the number of correct answers marked by four students in Mathematics test.

Answer the following questions:

1. Which of the student will get maximum marks in the mathematics test?
Answer: Krishna got 40 Marks in the mathematics test.

3. What is the difference between the number of questions marked correctly by Krishna and Yamini?
Answer: 15 difference between the number of questions marked correctly by Krishna and Yamini

NCERT Workbook Solutions For Class 3 Chapter 9 Patterns And Symmetry

Concept Review Introduction

We can see a lot of patterns in nature. Patterns are designs which follow a similarity or repetition. These can be figures, numbers or letters.

• Understanding number patterns in math helps us to develop our mental skills and relationships. Patterns give a sense of order and aesthetics.
• Similarly, shapes have symmetry when you draw a line that divide them in equal parts. A circle is same on both sides if you fold it along its diameter.

Read and Learn More Class 3 Workbook Solutions

NCERT Workbook Solutions For Class 3 Patterns And Symmetry Patterns

patterns are continuous repetitions. we can see many patterns in nature and manmade objects around us.

Patterns In Nature

Man-made Patterns

Number Patterns

Pattern In Numbers Can Be Based On Any One Of The Operations- Addition, Subtraction, Multiplication Or Division. It Can Also Be A Combination Of The Operations.

Question 1. Observe the given sequence. 12, 14, 16, ? What will be the next number in place of (?) in the series?
Answer:

12 + 2 = 14, 14 + 2 = 16, 16 + 2 = 18

The missing number is 18.

Question 2. Complete the pattern. 1, 4, ?, 16
Answer: 1, 1+ 3 = 4, 4+ 5 = 9, 9 +7 = 16

The missing number is 9.

Question 3. Observe the series given below and find the missing number. 55, 66, 77, ?
Answer: 11 × 5, 11 × 6, 11 × 7, 11 × 8 = 88

The missing number is 88.

Question 4. Complete the given series. 300, 250, ?, 150
Answer:

300-50=250, 250-50=200, 200-50=150

The missing number is 200.

Patterns in addition and multiplication are called growing patterns and the value of the numbers increases. Patterns in subtraction and division are called shrinking patterns as the value in these patterns keeps decreasing.

Letter patterns

Patterns can be formed with the letters of the English alphabet.

Question 5. Observe the given sequence and find the missing set of alphabets.
Answer:

1. A → Next alphabet B is repeated twice
2. After B it is C Next alphabet D is repeated twice
3. After D it is E Next alphabet F is repeated twice.

The missing pattern is EFF

ln letter pattern, numbers can be included by learning position of English alphabets

Question 6. If MOON is written as 13151514, then how position of PLANET is written?
Answer:

Planet is written as 1612114520

Patterns In Figures

We can find patterns even in figures. The missing pattern can be found by understanding the rule in the pattern

The missing pattern is

Question 7. Complete the pattern:

Answer:

ln the given pattern of figures,

Step 1-Six triangles

Step2-Five triangles

Step3-Four triangles

Step4-Three triangles

Step 5 – It should be two triangles, as

NCERT Workbook Solutions For Class 3 Patterns And Symmetry Patterns

Question 1. Choose the correct alternative.

1. Complete the series. 14, 11, 13, 10,12, ▭, ▭

1. 11, 9
2. 9, 11
3. 10, 8
4. 8, 10

Answer: 2. 9, 11

2. Find the missing number in the given pattern of figures

1. 129
2. 130
3. 63
4. 145

Answer: 3. 63

3. If 19-21-14 is ‘SUN’, then 13-1-18-19 is

1. Nest
2. Mars
3. Best
4. Fast

Answer: 2. Mars

5. Complete the following growing pattern.

Answer: 4.

6. Find the value of A, B and C in the given pattern.

Answer: 3.

8. Give the next two terms of the given series.

ACE FHJ KMO ____, _____

1. PRT, UWY
2. PRS, TVX
3. QSU, VXZ
4. NPR, SUW

Answer: 2. PRS, TVX

Question 2 . State whether the following statements are True or False.

1. If we start with 14 and skip count by 10, two places after 14 will be 44
Answer: False

2. Decreasing patterns are formed by subtraction and division of numbers.
Answer: True

Question 4. Fill in the blanks

Spot the pattern and then fill in the missing patterns.

1. Write the next 3 numbers in this pattern

Answer: 1, 2, 3

Question 5. Very Short Answer Type Questions.

1. Make the series by following the pattern:

1. AZCYEX  __________

Answer:

1. AZCYEXGWIVKVMUOTQSR

2. Complete the given pyramids. First one is given as an example

Answer:

3. Draw next figure in the given patterns.

Answer:

NCERT Workbook Solutions For Class 3 Patterns And Symmetry Symmetry

The Balanced, Proportional, Similarity Found On Two Halves Of An Object Is Called Symmetry. One Half Will Be The Mirror Image Of The Other. We Can Find Symmetry In Different Shapes In Our Daily Life.

Symmetry Along A Line

The imaginary line through which a shape or object is symmetrical, is called the line of symmetry. The object has exactly two mirror halves along the line of symmetry.

Symmetry In Alphabets Of English

Reflection Symmetry

When one half of an image or object is exact reflection of the other half, it is called reflection symmetry. It can be along a vertical or horizontal plane.

When there is a difference between the object and its image, then there is no symmetry. Generally, the left and right sides of an object appear inverted in the mirror image. Letters written from right to left appear left to right in a mirror image.

Tessellation

Tessellation Or Tiling Is Covering A Surface Using One Or More Geometric Shapes Repeatedly, Without Any Overlap. One Can See Them In Floors Or Walls.

Tiling With Geometrical Shapes

NCERT Workbook Solutions For Class 3 Patterns And Symmetry Symmetry

Question 1. Choose the correct alternative.

1. Identify the symmetrical pair of

Answer: 3.

2. Identify the number which has both horizontal and vertical symmetry

1. 10
2. 3
3. 8
4. 9

Answer: 3. 8

3. Identify the word which is its own mirror image.

1. WON
2. SUN
3. DO
4. MOM

Answer: 4. MOM

4. The total number of shaded squares with the mirror image will be?

1. 10
2. 12
3. 14
4. 16

Answer: 4. 16

5. The polygon formed by mirror image of the figure  is

1. Pentagon
2. Rectangle
3. Hexogen
4. Square

Answer: 1. Pentagon

Question 2. Match the Column-1 with Column-2.

Identify the symmetrical shapes

1. 1 → (D), 2 → (A), 3 → (B), 4 → (E),  5 → (C)
2. 1 → (C), 2 → (A), 3 → (E), 4 → (2), 5 → (D)
3. 1 → (E),   2 → (A), 3 → (D), 4 → (B), 5 → (C)
4. 1 → (B),  2 → (D), 3 → (A), 4 → (E), 5 → (C)

Answer: 1. 1 → (D), 2 → (A), 3 → (B), 4 → (E), 5 → (C)

Question 3. State whether the following statements are True or False.

1. Circle has infinite lines of symmetry
Answer: False

2. All objects have a symmetrical mirror image.
Answer: True

Question 4. Very Short Answer Type questions.

1. Write the number of symmetrical parts in the given shape.

_________ Two Symmetry

__________ Four Symmetry