PW Class 7 Maths Notes Chapter 8: Working With Fractions

Fractions are used to represent parts of a whole, but working with them becomes more challenging when you need to compare, simplify, add, subtract, multiply, or divide different fractions. Unlike fractions may require extra steps, while mixed numbers and reciprocals can also make calculations confusing if the rules are not clear.

PW Class 7 Maths Chapter 8 Notes bring these concepts together with simple explanations, important rules, and solved examples. You can use these notes to understand fraction operations step by step, revise key methods, and become more comfortable solving questions involving fractions.

What Does a Fraction Represent?

A fraction represents a part of a whole or a part of a group. It is written in the form:

ab\frac{a}{b}

• Numerator: The number above the line, which shows the parts being considered.

• Denominator: The number below the line, which shows the total equal parts.

• Example: In 1/4, 1 is the numerator, and 4 is the denominator.

When Are Fractions Called Equivalent?

Different-looking fractions can represent the same value. Such fractions are called equivalent fractions.

For example:

1/2=2/4=4/8

These fractions look different, but each represents the same part of a whole.

How Can You Find the Simplest Form of a Fraction?

A fraction is in its simplest form when its numerator and denominator have no common factor other than 1.

For example:

8/24=4/12=2/6=⅓

 Therefore, the simplest form of 8/24 is: 1/3

How Do You Add and Subtract Like Fractions?

Like fractions have the same denominator. To add or subtract them:

1. Keep the denominator unchanged.

2. Add or subtract the numerators.

3. Simplify the answer if needed.

Addition

1/5+2/5=⅗

 Subtraction

3/4−2/4=1/4

 What Steps Are Used for Unlike Fractions?

Unlike fractions have different denominators. Before adding or subtracting them, convert them into equivalent fractions with a common denominator.

For example:

5/6−1/4

The LCM of 6 and 4 is 12.

5/6=10/12 1/4=3/12

Therefore,

5/6−1/4=10/12−3/12=7/12

Which Methods Are Used to Multiply Fractions?

Fractions can be multiplied by other fractions, whole numbers, and mixed numbers.

• Multiplication by Fractions

Multiply the numerators together and the denominators together.

1/2×3/4=1×3/2×4=3/8

• Multiplication by Whole Numbers

Write the whole number as a fraction with denominator 1.

3/8×2 =3/8×2/1=6/8=3/4

• Multiplication by Mixed Numbers

First, convert the mixed numbers into improper fractions.

323×4153\frac{2}{3}\times4\frac{1}{5} =113×215=\frac{11}{3}\times\frac{21}{5} =23115=15615=1525=\frac{231}{15} =15\frac{6}{15} =15\frac{2}{5}

Does the Order Matter When Multiplying Fractions?

Changing the order of two fractions while multiplying does not change the final answer. This is known as the commutative property of multiplication.

For example:

12×14=18\frac{1}{2}\times\frac{1}{4} =\frac{1}{8}

and

14×12=18\frac{1}{4}\times\frac{1}{2} =\frac{1}{8}

Therefore,

ab×cd=cd×ab\frac{a}{b}\times\frac{c}{d} = \frac{c}{d}\times\frac{a}{b}

Why Is the Reciprocal of a Fraction Important?

The reciprocal of a fraction is found by interchanging its numerator and denominator. It is also called the multiplicative inverse.

For example:

Multiplying a non-zero fraction by its reciprocal gives 1:

35×53=1515=1\frac{3}{5}\times\frac{5}{3} =\frac{15}{15} =1

How Do You Divide One Fraction by Another?

Fraction division can be solved by multiplying the first fraction by the reciprocal of the second fraction. A useful way to remember the process is keep, change, flip.

For example:

23÷35\frac{2}{3}\div\frac{3}{5}

Keep: Keep the first fraction unchanged.

23\frac{2}{3}

Change: Change division into multiplication.

23×\frac{2}{3}\times

Flip: Take the reciprocal of the second fraction.

53\frac{5}{3}

Therefore,

23×53=109\frac{2}{3}\times\frac{5}{3} =\frac{10}{9}

Class 7 Maths Chapter 8 Notes PDF

You can use PW Class 7 Maths Chapter 8 Notes to revise the important concepts of Working With Fractions in one place. The notes cover fraction basics, equivalent fractions, simplification, addition, subtraction, multiplication, reciprocals, and division.

Why Choose PW Notes for Class 7 Maths Chapter 8?

Physics Wallah Class 7 Maths Chapter 8 Notes help you study Working With Fractions through clear explanations, key rules, and useful examples. They can make it easier to understand fraction operations and revise the chapter before solving questions.

• Clear Fraction Concepts: Understand numerators, denominators, equivalent fractions, and simplest forms with easy explanations.

• Easy Methods for Operations: Learn the steps for adding, subtracting, multiplying, and dividing fractions.

• Support for Different Question Types: Revise methods for working with like fractions, unlike fractions, whole numbers, and mixed numbers.

• Quick Revision of Key Rules: Recall important concepts such as reciprocals and the commutative property of multiplication.

• Step-by-Step Examples: Follow solved examples to understand how each fraction operation is carried out.

• Better Concept Recall: Bring important definitions, rules, and methods together for convenient revision.

• Confidence in Problem-Solving: Strengthen your understanding before attempting NCERT exercises and other fraction-based questions.

Working with fractions becomes easier when you understand the rule behind each operation and apply it step by step. This chapter takes you from basic fraction concepts to addition, subtraction, multiplication, reciprocals, and division. PW Class 7 Maths Chapter 8 Notes give you a convenient way to revisit these methods, clear your concepts, and practise fraction-based questions with confidence.

Related Resources

• CBSE Class 7 Maths NCERT Solutions

• CBSE Class 7 Maths Sample Papers

• CBSE Class 7 Maths Most Important Questions

• CBSE Class 7 Maths Notes