Class 4 — Mathematics

Fractions: Equivalent Fractions and Addition/Subtraction of Like Fractions

Class 4

✓By the end of this lesson students will be able to identify and define equivalent fractions.
✓By the end of this lesson students will be able to find equivalent fractions by multiplying or dividing the numerator and denominator by the same non-zero number.
✓By the end of this lesson students will be able to define like fractions.
✓By the end of this lesson students will be able to add two or more like fractions.
✓By the end of this lesson students will be able to subtract a like fraction from another like fraction.

Key concepts

Fractions (Recap)

A fraction represents a part of a whole. It has a numerator (the top number) and a denominator (the bottom number). The denominator tells us the total number of equal parts the whole is divided into, and the numerator tells us how many of those parts are being considered.

Equivalent Fractions

Equivalent fractions are fractions that represent the same value or the same part of a whole, even though they may look different. We can find equivalent fractions by multiplying or dividing both the numerator and the denominator by the same non-zero number.

a/b = (a × c) / (b × c) OR a/b = (a ÷ c) / (b ÷ c) (where c is a non-zero number)

Like Fractions

Like fractions are fractions that have the same denominator.

Addition of Like Fractions

To add like fractions, we add their numerators and keep the denominator the same.

a/c + b/c = (a + b) / c

Subtraction of Like Fractions

To subtract like fractions, we subtract their numerators and keep the denominator the same.

a/c - b/c = (a - b) / c

Key facts to remember

1A fraction represents a part of a whole.
2Equivalent fractions represent the same value, even if they look different.
3To find equivalent fractions, multiply or divide both the numerator and denominator by the same non-zero number.
4Like fractions are fractions that have the same denominator.
5To add like fractions, add the numerators and keep the denominator the same.
6To subtract like fractions, subtract the numerators and keep the denominator the same.
7Always simplify fractions to their lowest terms if possible.

Worked examples

Example 1

Find two equivalent fractions for 3/5.

ITo find the first equivalent fraction, multiply both the numerator and the denominator by 2.

II3/5 = (3 × 2) / (5 × 2) = 6/10.

IIITo find the second equivalent fraction, multiply both the numerator and the denominator by 3.

IV3/5 = (3 × 3) / (5 × 3) = 9/15.

Answer

Two equivalent fractions for 3/5 are 6/10 and 9/15.

Example 2

Add 2/7 and 3/7.

ISince these are like fractions (they have the same denominator, 7), we add their numerators and keep the denominator the same.

II2/7 + 3/7 = (2 + 3) / 7

III= 5/7

Answer

5/7

Example 3

Subtract 1/9 from 7/9.

ISince these are like fractions (they have the same denominator, 9), we subtract their numerators and keep the denominator the same.

II7/9 - 1/9 = (7 - 1) / 9

III= 6/9

IVWe can simplify this fraction by dividing both the numerator and denominator by their common factor, 3.

V6/9 = (6 ÷ 3) / (9 ÷ 3) = 2/3.

Answer

2/3

Always try to simplify your answer to its simplest form if possible.

Common mistakes

✗Adding or subtracting the denominators when adding or subtracting like fractions.
✗Multiplying the numerator by one number and the denominator by a different number when finding equivalent fractions.
✗Forgetting to simplify the final answer to its simplest form.
✗Confusing like fractions with unlike fractions.

Exam tips

★Read the question carefully to understand if you need to find equivalent fractions, add, or subtract.
★Show all your steps clearly, especially when finding equivalent fractions or simplifying.
★Double-check your calculations for addition and subtraction.
★Always look for common factors to simplify your final answer.

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