Adding and subtracting fractions: what children learn
In the game, children balance the scales: they find the fraction that makes both sides equal, such as 2/9 + 5/9 = ? or 2/9 + ? = 7/9. The Quick quiz 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.
Supports part of Common Core 4.NF.B.3.a. This focused game does not cover the entire standard.
Common Core connection: 4.NF.B.3.a. This is focused practice for part of the standard.
How to play
Make both sides of the scales equal. Tap the weight that fills the gap, or press 1 to 4. Each game has 8 questions and no timer. If a weight doesn't balance, the scales tip towards the heavier side and you get one more try. You get a point for each one balanced first time. For a quicker go, choose Quick quiz: 10 multiple-choice questions in 120 seconds (choose Relaxed for more time).
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.
- Recognize 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 recognizing 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 liter.
- 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 students to find all the pairs of sixths that add up to one whole.
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
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.
How should I choose this game for my learner?
Supports part of Common Core 4.NF.B.3.a. This focused game does not cover the entire standard.
How should I choose this game for my learner?
Supports part of Common Core 4.NF.B.3.a. This focused game does not cover the entire standard.