Primary 6 · Mathematics

P6 fractions

Dividing a fraction by a whole number should make it smaller, but a half-remembered rule often makes it bigger. Here is the one sentence where three-quarters turns into one and a half instead of three-eighths.

Level
P6
Usually taught
Term 1
Covers
1 concept

What changes at P6

At Primary 6, fractions get divided, not just added and multiplied. Your child divides a fraction by a whole number, and later a whole number by a fraction. The arithmetic is small. The understanding is the part that costs marks.

It all turns on one idea: dividing shares a fraction into smaller pieces. Three-quarters divided by 2 is three-eighths, not one and a half. A child who divides by multiplying the whole number gets a bigger answer and does not notice anything is wrong.

The sentence that costs the mark

Work out 34÷2\frac{3}{4} \div 2.

What the working usually does

2 times34\frac{3}{4}=1121\frac{1}{2}

Two times three-quarters. But dividing by 2 shares it out, so the answer has to be smaller than 3/4, and 1½ is bigger.

What the question asked

half of34\frac{3}{4}=38\frac{3}{8}

Half of three-quarters. Split each quarter into two and you get eighths, so 3/4 is 6/8, and half of that is 3/8.

Flip and multiply is a real rule the child has heard, and 1½ is a tidy answer, so the working looks finished. The only tell is the sense-check: dividing by 2 must make three-quarters smaller, and 1½ is bigger.

Three-quarters is six eighths. Shared between two, each piece is three eighths, smaller than the three-quarters you started with.

The same question, worked properly

  1. Dividing must make it smaller

    answer <34< \frac{3}{4}

    Dividing by 2 shares the three-quarters into two, so each part is smaller than you started with. If the answer comes out bigger, something has gone wrong before the arithmetic even matters.

  2. Share each quarter into two

    34=68\frac{3}{4} = \frac{6}{8}

    This is the step that fails. Split every quarter into two and the pieces become eighths, so three-quarters is six eighths. This is the step where a memorised flip and multiply misfires into 2 times, giving 1½, bigger not smaller.

  3. Take one share

    half of 68\frac{6}{8} = 38\frac{3}{8}, so 34÷2=38\frac{3}{4} \div 2 = \frac{3}{8}

    One of the two equal shares is three eighths. Sense-check, and it passes: 3/8 is smaller than 3/4.

  4. Why flip and multiply works

    34÷2=34×12=38\frac{3}{4} \div 2 = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}

    Dividing by 2 is the same as taking a half. Flipping the 2 to a half is the reason the rule gives the right answer, not a piece of magic to memorise.

How can you tell it has clicked?

You do not need to do the fraction maths to check this. When your child divides a fraction by a whole number, ask one thing first: should the answer be bigger or smaller than what you started with?

Dividing by 2 shares it into two, so each part is smaller. A child who says "smaller" has understood the idea. A child whose answer came out bigger has run a rule without checking whether it made any sense.

One thing to try tonight

Three-quarters of a pizza, shared between two people. Before working anything out, ask: does each person get more than three-quarters, or less? Less, of course, because you are splitting it up.

Then the maths matches the sense: three-quarters shared by two is three-eighths each. If their working ever gives a bigger answer than they started with, that is the signal to stop and look again.

What your child will meet in this topic

  • Fraction ÷ Whole

Most Singapore schools introduce this in Term 1, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.

What it leads to

Dividing fractions is the last rung of the fraction ladder that runs all the way from P3. It feeds straight into ratio and rate, where a quantity is shared or scaled and the same "bigger or smaller?" check keeps working.

A child who divides by understanding, sharing into smaller pieces, carries that into secondary school. A child running flip and multiply blind loses marks the moment the numbers stop being friendly.

The methods your child will use here

Each one is the same method wherever it turns up, so it is worth learning once.

The same topic in other years

It comes back each year and gets harder, so it helps to see what came before and what is coming.

More in Primary 6

Other topics in the same year, so you can see what sits either side of this one.

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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