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How to explain equivalent fractions to kids
Equivalent fractions are different names for the same amount. Half a sandwich is the same as two quarters of the sandwich: 1/2 = 2/4. The amount stays the same. Only the number of pieces changes.
The best way to explain it is to let your child see it happen, then show the rule. If they learn the rule first, it can feel like a trick that changes the number.
Three ways to show it
- Fold paper. Fold a strip in half and shade one half. Fold it in half again. Now there are 4 pieces and 2 are shaded: 1/2 = 2/4. Fold again: 1/2 = 4/8.
- Number line. Draw thirds and sixths on two lines of the same length. The 2/3 mark lines up with 4/6, so 2/3 = 4/6.
- The rule. Splitting every piece into 4 makes 4 times as many pieces, and 4 times as many shaded. So multiply the top and bottom by the same number: 2/3 = 8/12.
6 practice questions: fill in the missing number
- 1/2 = ?/6
- 1/3 = ?/9
- 3/4 = ?/8
- 2/5 = ?/10
- 3/5 = ?/15
- 5/6 = ?/12
Show answers
- 1/2 = 3/6
- 1/3 = 3/9
- 3/4 = 6/8
- 2/5 = 4/10
- 3/5 = 9/15
- 5/6 = 10/12
Tips for parents
- Always multiply (or divide) the top and bottom by the same number. Adding the same number doesn't work.
- Ask "is it still the same amount?" after each step.
- Practice simplifying too. It's the same idea in reverse.
Questions parents ask
What grade learns equivalent fractions?
Children meet simple equivalent fractions in 3rd grade and learn the multiply-top-and-bottom rule in 4th grade, in the US Common Core standards.