Why do we flip and multiply to divide fractions? How to explain it to a child
A child who asks "why?" is doing something good. Thinking about how many parts fit inside is easier to remember than a rule on its own.
Start with a question
What does 2 ÷ 1/4 mean? Ask your child: "Two pizzas, each serving a quarter of a pizza. How many servings is that?"
Each pizza makes 4 servings, so 2 pizzas make 8. So 2 ÷ 1/4 = 8, which is 2 × 4. Dividing by a quarter is the same as multiplying by 4.
Then when the numerator isn't 1
What about 2 ÷ 2/3? Each serving is two-thirds of a pizza. If each were one-third, 2 pizzas would make 2 × 3 = 6 servings. Each serving is now twice as big, so there are half as many: 6 ÷ 2 = 3.
Together, those two steps are 2 × 3/2 = 3, which is "flip and multiply". The flipped fraction, 3/2, is called the reciprocal of 2/3.
Common mistakes
- Flipping the first fraction. Only flip the divisor, the one after the ÷.
- Forgetting to change ÷ to ×.
- Expecting a smaller answer. Dividing by a number less than 1 makes the answer bigger, and this is the most worthwhile thing for a child to understand.
If your child can't see it yet
Older primary children are starting to handle more abstract ideas, but still need concrete examples to lean on. If your child can't see it yet, go back to the pizzas and pictures. That doesn't mean a lack of ability.
Being able to say why often matters more than getting one answer right, as this is how children build thinking habits and confidence. Ask your child to explain the method to you.
