Simplifying fractions: what children learn
In the game, children balance the scales with equivalent fractions, such as 12/18 = ?/3 or 3/4 = 9/?. In the Quick quiz, each question shows a fraction to simplify, with four choices. Watch out: sometimes one of the wrong choices is equal in value but only partly simplified (such as 6/9 for 12/18). It is a fair fraction, but not the simplest form, so it is not the answer.
Supplemental equivalent-fraction practice. Common Core 4.NF.A.1 focuses on explaining equivalence with models; this game practices simplification numerically.
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
- Find a common factor. Look for a number that divides both the numerator and the denominator. 12 and 18 are both even, so 2 is a common factor.
- Divide both numbers by it. 12 ÷ 2 = 6 and 18 ÷ 2 = 9, so 12/18 = 6/9.
- Keep going until you can't. 6 and 9 share the factor 3: 6/9 = 2/3. 2 and 3 have no common factor except 1, so 2/3 is the simplest form.
- Or use the highest common factor. The highest common factor (HCF) of 12 and 18 is 6. Dividing both by 6 gets to 2/3 in one step.
Worked examples
Example 1: Simplify 15/20.
Working: Both are in the 5 times table: 15 ÷ 5 = 3, 20 ÷ 5 = 4.
Answer: 3/4
Example 2: Simplify 24/36.
Working: HCF is 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3. (Dividing by 2 first gives 12/18, which still simplifies.)
Answer: 2/3
Example 3: Simplify 7/21.
Working: 7 is a factor of both: 7 ÷ 7 = 1, 21 ÷ 7 = 3.
Answer: 1/3
Common mistakes and how to fix them
- Stopping too early: 24/36 simplified to 12/18. After each step, check whether the new numbers still share a factor.
- Dividing the numerator and denominator by different numbers. Both must be divided by the same number, or the value of the fraction changes.
- Subtracting instead of dividing (thinking 5/8 simplifies to 2/5 by taking 3 from each). Simplifying only ever uses division by a common factor.
Activities to try at home
- Look at fractions in recipes or measurements: is 4/8 of a cup the same as ½?
- Fold paper to show that 2/4, 3/6 and 4/8 cover the same area as ½.
- Play 'snap' with equivalent fraction cards.
Ideas for the classroom
- Use fraction walls to show families of equivalent fractions.
- Ask students to list the factors of the numerator and denominator and circle the highest common factor.
- Link to adding fractions with different denominators, where simplifying the answer is the last step.
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
What does simplest form mean?
The numerator and denominator have no common factor other than 1. For example, 2/3 is in simplest form, but 4/6 is not.
How should I choose this game for my learner?
Supplemental equivalent-fraction practice. Common Core 4.NF.A.1 focuses on explaining equivalence with models; this game practices simplification numerically.
What is the US equivalent?
The closest Common Core standard is 4.NF.A.1 (Grade 4) on equivalent fractions. It does not set out 'simplest form' as a separate standard.