NCERT Workbook Solutions For Class 3 Chapter 7 Fractions

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