Adding and subtracting fractions: what children learn
Year 3 pupils learn to add and subtract fractions with the same denominator within one whole, for example 5/7 + 1/7 = 6/7. When the denominators are the same, every part is the same size, so you just count how many parts you have.
The game shows questions such as 2/9 + 5/9 = ? and 7/8 − 3/8 = ? with four answer choices. One wrong choice always shows the classic mistake of adding the denominators as well (2/9 + 5/9 = 7/18). Answers stay within one whole, and if the total is exactly one whole, such as 3/5 + 2/5, the answer is shown as 1.
This topic covers the Year 3 statutory requirement in the National Curriculum in England (Number – fractions): pupils should be taught to “add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7]”. Year 3 pupils are usually aged 7–8.
For families following US standards, the closest Common Core standard is 4.NF.B.3.a, which is taught in Grade 4. Common Core adds fractions with like denominators in Grade 4.
How to play
Answer 10 questions before the clock runs out. Tap an answer, or press 1 to 4. Each game has 10 multiple-choice questions and a 120-second timer. A wrong answer shows the correct one before moving on. You earn up to three stars depending on your score.
Step by step
- Check the denominators match. This method only works when the bottom numbers are the same, for example sevenths and sevenths.
- Add or subtract the numerators. 2/7 + 3/7: two sevenths and three sevenths make five sevenths. 2 + 3 = 5.
- Keep the denominator. The size of each part does not change, so the denominator stays 7. The answer is 5/7.
- Recognise one whole. If the numerator equals the denominator, as in 7/7, the answer is one whole.
Worked examples
Example 1: 2/9 + 5/9 = ?
Working: 2 ninths + 5 ninths = 7 ninths.
Answer: 7/9
Example 2: 7/8 − 3/8 = ?
Working: 7 eighths take away 3 eighths leaves 4 eighths.
Answer: 4/8 (which is also equal to ½)
Example 3: 3/5 + 2/5 = ?
Working: 3 fifths + 2 fifths = 5 fifths, which is one whole.
Answer: 1
Common mistakes and how to fix them
- Adding the denominators: 2/7 + 3/7 = 5/14. Say the fractions in words: 'two sevenths plus three sevenths'. Sevenths stay sevenths, just like 2 apples + 3 apples is 5 apples, not 5 'double apples'.
- Subtracting the denominators: 5/8 − 2/8 = 3/0. Draw a bar in eighths and cross out the parts being taken away.
- Not recognising 6/6 as 1. Shade all the parts of a bar: the whole bar is one whole.
Activities to try at home
- Use a chocolate bar or pizza cut into equal pieces: 2 eighths eaten plus 3 eighths eaten is 5 eighths eaten.
- Fill a measuring jug in quarters of a litre.
- Make up fraction stories: 'I walked 3/10 of the way, then 4/10 more. How far have I walked?'
Ideas for the classroom
- Use fraction walls and bar models to show adding parts of the same size.
- Count up and down in fractions on a number line: 1/5, 2/5, 3/5…
- Ask pupils to find all the pairs of sixths that add up to one whole.
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
Why don't you add the denominators?
The denominator tells you the size of each part. Adding fractions of the same size doesn't change the size of the parts, only how many you have.
Do answers need to be simplified?
Not in Year 3. 4/8 is a correct answer. Simplifying fractions is a Year 6 objective, and the game does not offer an equivalent fraction such as ½ as a separate choice.
Is this taught in Year 3 in the US?
In the Common Core, adding fractions with like denominators is standard 4.NF.B.3.a, in Grade 4.