NCERT Workbook Solutions For Class 3 Chapter 3 Multiplication And Division

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