Primary 6 · Number & Algebra

P6 fractions

In P6, your child divides a fraction by a whole number, then divides by a fraction. Dividing by a whole number shares the fraction out, so the answer must come out smaller.

Taught in
Term 1
Syllabus
2 skills
Usual slip
Multiplying by the 2

Three quarters cut into eighths and shared into two shares of three eighths

What your child learns in P6 fractions

Two skills, each with what it looks like on a worksheet.

Follows the latest (2026) MOE syllabus
See the syllabus wording
  • dividing a proper fraction by a whole number without calculator
  • dividing a whole number/proper fraction by a proper fraction without calculator

A fraction divided by a whole number

Dividing shares the fraction into equal parts, so each part is smaller. 3/8 ÷ 3 = 1/8: three eighths shared by 3 is one eighth each. If the top does not share evenly, cut each piece smaller first.

3/8 ÷ 3 = 1/8

Dividing by a fraction

Now ask how many of the fraction fit. 3 ÷ 1/2 = 6, because each whole holds 2 halves. A fraction divided by a fraction works the same way: count how many fit.

3 ÷ 1/2 = 6

Key facts and formulas

Term 1
  • Fraction ÷ whole number: share it out34÷2=\frac{3}{4} \div 2 = 38\frac{3}{8}
  • Whole ÷ fraction: how many fit?2÷23=2 \div \frac{2}{3} = 33
  • ÷ a fraction: Keep, Change, Flip34÷38=\frac{3}{4} \div \frac{3}{8} = 34×83=\frac{3}{4} \times \frac{8}{3} = 22

Words to know

Share
Split into equal parts. Dividing by 2 shares into 2 parts.
Equal parts
Pieces of exactly the same size.
Reciprocal
The number flipped. ÷ 2 is the same as × 1/2.
Simplest form
The fraction with the smallest top and bottom, such as 1/6 for 2/12.

The sentence that costs the mark

Find the value of 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.

The same P6 fractions question, worked properly

Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.

A gardener watered 23\frac{2}{3} of a field in 4 hours. He watered an equal amount each hour. What fraction of the field did he water each hour?

Step 1 of 4▌
  1. Draw the field as one bar of 3 equal units, and shade 2 for the 23\frac{2}{3} watered. Sharing it over 4 hours makes each share smaller.
  2. Never multiply by 4, which gives more than the whole field. Cut each unit into 2, so 23\frac{2}{3} = 46\frac{4}{6}.
  3. The 4 watered units are shared over 4 hours, so each hour gets 1 of the 6 units: 23\frac{2}{3} ÷ 4 = 16\frac{1}{6}.
  4. So he watered 16\frac{1}{6} of the field each hour.

Every question in StudyLah comes with a walkthrough like this one.

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Two quick P6 fractions questions

Try them together, then tap to check.

Question 1

Find 67÷4\frac{6}{7} \div 4. Express your answer in its simplest form.

Show answer

Answer314\frac{3}{14}. Sharing 6 sevenths into 4 parts makes each piece smaller: 67\frac{6}{7} ÷ 4 = 628\frac{6}{28}, which is 314\frac{3}{14}.

Question 2

Rahmat used 56\frac{5}{6} of a roll of tape over 10 lessons. He used an equal length each lesson. What fraction of the roll did he use each lesson?

Show answer

Answer112\frac{1}{12}. 56\frac{5}{6} ÷ 10 shares 5 sixths over 10 lessons, so each lesson gets 560\frac{5}{60}, which is 112\frac{1}{12}.

Helping at home

How to tell it has clicked

Before your child divides a fraction by a whole number, ask: should the answer be bigger or smaller than what you started with? Smaller, because it is being shared.

An answer bigger than the starting fraction means a rule ran without a check. That is the moment to stop and look again.

Try this 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, because you are splitting it. Three-quarters shared by two is three-eighths each.

Before and after P6 fractions

  1. Builds on

    Primary 5 Fractions and Division

    Takes a fraction of what is left

  2. You are here

    Primary 6 Fractions

    Divides fractions into equal shares

The methods your child will use here

In the PSLE's hardest questions

More in Primary 6

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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