Class 7 Maths: making multiplying and dividing fractions make sense

Try this on yourself first: why does dividing by a half give you a bigger number? Most of us learned "flip and multiply" and never looked back. The rule works. It just doesn't explain anything, and children who only memorise it tend to lose it by the next exam. The Class 7 chapter "Working with Fractions" is a good moment to give the rules some pictures. You don't need to be confident at maths. You need paper, a pencil and a bit of curiosity.

Start with a folded sheet of paper

Fold a sheet into three equal strips and shade one. Now fold that strip in half and shade one half. What fraction of the whole sheet is shaded? Count the small pieces: it's 1/6. So half of a third is a sixth, which is exactly what 1/2 × 1/3 says.

Let your child find that out before you mention any rule. The rule, when it comes, will feel like something they already knew.

The four ideas behind it

• Multiplying fractions. Multiply the tops (numerators) and multiply the bottoms (denominators). So 2/3 × 3/5 = 6/15.
• Cancelling and lowest form. Dividing the top and bottom by the same number doesn't change the amount. 6/15 becomes 2/5. You can cancel before multiplying, which keeps the numbers small.
• Size sense. Multiplying by a number bigger than 1 makes a result bigger. Multiplying by a fraction less than 1 makes it smaller. Often you can guess roughly how big an answer will be before you calculate.
• Dividing fractions. Dividing by a fraction means multiplying by its flip, called the reciprocal. Dividing by a fraction smaller than 1 gives a bigger answer.

Guess before you calculate

Before any sum, ask: "Will 3/4 × 8 be more or less than 8?" Less, because you're taking part of 8. "Will 5 ÷ 1/2 be more or less than 5?" More, because there are lots of halves in 5. Ten, in fact. Make guessing first a habit. It catches silly mistakes before they reach the answer line.

The leftover cake

Draw a rectangle for a cake. Say 3/4 of it is left and four people share it fairly. Each person gets 3/4 ÷ 4, which is 3/16 of the whole cake. Ask your child to draw it and check by cutting the 3/4 into four equal pieces. Nobody argues with a drawing.

Cancel first, multiply later

Try 3/8 × 4/9. Ask your child to hunt for a top number and a bottom number that share a factor. The 3 and the 9 share 3, and the 4 and the 8 share 4. After cancelling, you get 1/2 × 1/3 = 1/6. Then do it the long way, 12/72, and reduce it to see the same answer. It's not a trick. It's the same amount, written with smaller numbers.

Three questions, with answers

Pencil allowed, book not.

1. Is 2/3 × 3/5 bigger or smaller than 3/5, and what is the answer in lowest form?
2. How many halves are there in 3? How is that the same as 3 ÷ 1/2?
3. Can you explain, in your own words, why cancelling doesn't change the answer?

For question 1, the answer is smaller, and 2/3 × 3/5 = 2/5. For question 2, six halves, and 3 × 2 = 6. If your child can explain the idea, the sums usually follow. If one question stumbles, draw a picture together next weekend.

Where the chapter breaks it down

The chapter is split into four ideas, each with a short explanation and a quick activity. Here's the page: Working with Fractions, Class 7 Mathematics. It also lists the quizzes and games that go with each idea.

If you want some practice questions

KRIGYAN has short quizzes and games for Class 7 Mathematics chapters like this one, though not every chapter is covered yet. It's free to try right now. Tell us which chapter your child is on, and we'll check it against what we have and let you know.