Why do we keep the denominator when adding fractions?

The pieces are the same size, so we only count how many pieces there are.

What are equivalent fractions?

Fractions that are worth the same amount, such as 1/2 and 4/8.

How do I turn 7/5 into a mixed number?

5/5 is 1 whole, so 7/5 = 1 and 2/5.

How do I simplify 6/8?

Divide the top and bottom by the same number. 6 / 2 = 3 and 8 / 2 = 4, so 6/8 = 3/4.

Year 4 adding and subtracting fractions lesson to download as PDF

This Year 4 adding and subtracting fractions lesson is written for pupils aged 8-9 and follows the National Curriculum. In short, it shows you how to add and subtract fractions with the same denominator and find equivalent fractions. Before you start, it helps to revise short multiplication and division and fractions and decimals: tenths and hundredths, because this lesson builds on them.

Table of Contents

Year 4 adding and subtracting fractions lesson: what you will learn

Hello, I am Otto! Fractions help us share things fairly and describe parts of a whole. In this chapter you learn to find equivalent fractions, to add and subtract fractions with the same denominator, to write answers bigger than one as mixed numbers, and to find fractions of amounts.

Starter activity

A pizza is cut into 8 equal slices. Maya eats 3 slices and Omar eats 2 slices. What fraction of the pizza have they eaten together? Each slice is one eighth. Maya ate three eighths and Omar ate two eighths. Together they ate 5 slices out of 8, which is five eighths. You added fractions without even noticing!

Numerator and denominator

Definition: fraction

A fraction shows equal parts of a whole. The bottom number is the denominator. It tells you how many equal parts the whole is cut into. The top number is the numerator. It tells you how many of those parts you have. In the fraction ³⁄₈, the whole is cut into 8 equal parts and we have 3 of them.

The circle is cut into 8 equal parts and 3 are shaded, so ³⁄₈ of the circle is shaded.

Key fact: unit fractions and non-unit fractions

A unit fraction has a numerator of 1, such as ¹⁄₂, ¹⁄₅ or ¹⁄₁₀.
A non-unit fraction has a numerator bigger than 1, such as ³⁄₄.
The bigger the denominator, the smaller each part is: ¹⁄₈ is smaller than ¹⁄₄.

Equivalent fractions

Definition: equivalent fractions

Equivalent fractions are fractions that have the same value but look different. For example ¹⁄₂ = ²⁄₄ = ⁴⁄₈. Half of a pizza is the same amount whether it is 1 slice out of 2 or 4 slices out of 8.

Look at the fraction wall. The bar for one half is exactly as long as two quarters, three sixths, four eighths or six twelfths. Fractions in the same position on the wall are equivalent.

Rule: making equivalent fractions

Multiply the numerator and the denominator by the same number and you get an equivalent fraction. For example ²⁄₃ = ⁴⁄₆ = ⁶⁄₉ (we multiply the top and bottom by 2 and by 3). You can also divide the top and bottom by the same number to make a simpler fraction: ⁶⁄₈ = ³⁄₄.

Example 1

Find the missing number: ³⁄₅ = ^?⁄₁₀.

The denominator goes from 5 to 10, so we multiply by 2. Multiply the numerator by 2 too: 3 × 2 = 6. So ³⁄₅ = ⁶⁄₁₀.

Adding and subtracting fractions with the same denominator

Rule: same denominators

When the denominators are the same, add or subtract only the numerators. The denominator stays the same because the size of the parts does not change. So ²⁄₇ + ³⁄₇ = ⁵⁄₇, not ⁵⁄₁₄.

3 eighths plus 2 eighths is 5 eighths.

Method: adding and subtracting fractions

Check that the denominators are the same.
Add or subtract the numerators.
Write the answer over the same denominator.
If the numerator equals the denominator the answer is 1 whole. If it is larger, write the answer as a mixed number.

Example 2

Work out ³⁄₈ + ²⁄₈ and ⁷⁄₁₀ − ⁴⁄₁₀.

Add the numerators and keep the denominator: 3 + 2 = 5, so ³⁄₈ + ²⁄₈ = ⁵⁄₈. Subtract the numerators and keep the denominator: 7 − 4 = 3, so ⁷⁄₁₀ − ⁴⁄₁₀ = ³⁄₁₀.

Watch out

Never add the denominators! If you eat ¹⁄₄ of a cake and then another ¹⁄₄, you have eaten ²⁄₄ (which is the same as ¹⁄₂), not ²⁄₈. The pieces are quarters before and after you add, so the denominator stays 4.

Mixed numbers

Definition: mixed number

A mixed number has a whole number part and a fraction part, such as 1 ³⁄₄. An improper fraction has a numerator bigger than the denominator, such as ⁷⁄₄. Both mean the same amount: ⁷⁄₄ is 1 whole and ³⁄₄.

Example 3

Work out ⁵⁄₆ + ⁴⁄₆.

Add the numerators and keep the denominator: 5 + 4 = 9, so ⁵⁄₆ + ⁴⁄₆ = ⁹⁄₆, which is 1 ³⁄₆ as a mixed number. We can see this because 9 sixths is 6 sixths (1 whole) and 3 sixths more, so 1 ³⁄₆. This is the same as 1 ¹⁄₂, since ³⁄₆ = ¹⁄₂.

Fractions of amounts

Method: finding a fraction of an amount

Divide the amount by the denominator to find one part (the unit fraction).
Multiply by the numerator to find the required number of parts.
Write the answer with the correct unit.

Example 4

Find ³⁄₄ of 20, and ²⁄₅ of £30.

¹⁄₄ of 20: 20 ÷ 4 = 5. So ³⁄₄ of 20 is 3 × 5 = 15. ¹⁄₅ of £30: 30 ÷ 5 = 6. So ²⁄₅ of £30 is 2 × 6 = £12.

Example 5

A class has 28 children. ³⁄₇ of them walk to school. How many children walk? How many do not?

¹⁄₇ of 28 is 28 ÷ 7 = 4. So ³⁄₇ of 28 is 3 × 4 = 12 children walk. The rest do not walk: 28 − 12 = 16 children. Check: ⁴⁄₇ of 28 = 4 × 4 = 16.

Did you know?

The ancient Egyptians wrote almost all their fractions as unit fractions, such as ¹⁄₂, ¹⁄₃ and ¹⁄₄. They wrote ³⁄₄ as ¹⁄₂ + ¹⁄₄. The word fraction comes from a Latin word that means "broken", because a fraction is a broken piece of a whole.

Otto's tip

If you are not sure about a fraction question, draw a bar and split it into equal parts. Shade the parts you need. The picture often shows the answer before you calculate! Also remember: the bottom number names the parts, so it never changes when you add or subtract.

How to use this Year 4 adding and subtracting fractions lesson

First, read the key points so that you know where the Year 4 adding and subtracting fractions lesson is going. Then work through each definition and worked example, and cover the solution before you read it. After that, practise with the adding and subtracting fractions worksheet and check every question with the worksheet answers. When you feel ready, test yourself with the multiple choice questions or the quick quiz. Finally, sit the adding and subtracting fractions test and mark it with the test answers.

Also, the starters are a good warm-up, so you can keep the key facts fresh. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, this Year 4 adding and subtracting fractions lesson gives you everything you need for the chapter.