Dividing with Fractions

Dividing by a fraction sounds scary, but it is really just asking "how many of these small pieces fit inside?" How many half-cups of rice fit in 3 cups? How many quarter-metre ribbons can you cut from a long strip? Once you see division this way, the famous "flip and multiply" trick will make complete sense. Let's cut it down to size.

Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a PSLE marker rewards in the working — not just the final number.

By the end you'll be able to divide a whole number by a fraction, a fraction by a whole number, and a fraction by a fraction. Let's begin.

A whole number divided by a fraction

Dividing 3 by one half asks "how many halves fit into 3?" Each whole has 2 halves, so 3 wholes hold 6 halves. That is why dividing by one half is the same as multiplying by 2. We use the reciprocal, which is the flipped fraction.

So 3 ÷ one half = 3 × 2 (the flip of one half) = 6. Picture 3 litres of soup poured into half-litre bowls — you fill 6 bowls. Dividing by a number smaller than 1 gives a bigger answer, which feels odd until you picture the bowls.

A fraction divided by a whole number

Now the other way. Dividing one half by 3 means sharing half a thing among 3 people. Each person gets a smaller slice — one sixth. The rule: dividing by a whole number is the same as multiplying by its reciprocal, so dividing by 3 means multiplying by one third.

So one half ÷ 3 = one half × one third = one sixth. Imagine half a pizza shared by 3 friends — each gets one sixth of the whole pizza. Dividing by a whole number makes the fraction smaller.

A fraction divided by a fraction

The biggest one: a fraction divided by a fraction. The rule is the same — flip the second fraction and multiply. Dividing three quarters by one eighth asks "how many one-eighth pieces fit in three quarters?"

Flip one eighth to get 8, so three quarters ÷ one eighth = three quarters × 8 = 24 over 4 = 6. There are 6 eighth-pieces in three quarters. Always flip the SECOND fraction, the one you are dividing by — never the first.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. How many one-quarter pieces fit into 2 wholes?

   82One half

2. What is 4 divided by one half?

   28Two

3. What is one half divided by 4?

   One eighth2Two

4. What is two thirds divided by 2?

   One thirdFour thirdsTwo sixths only

5. What is three quarters divided by one quarter?

   3Three sixteenthsOne half

6. A ribbon is three quarters of a metre long. How many one-eighth-metre pieces can be cut from it?

   63Three thirty-seconds

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