Primary 3 · Number & Algebra

P3 fractions

In P3, your child finds equivalent fractions, writes a fraction in its simplest form, and compares and orders fractions. They also add and subtract fractions within one whole, both like fractions and unlike ones such as halves and quarters.

Taught in
Term 3
Syllabus
4 skills
Usual slip
Bigger bottom wins

Two equal bars, one third shaded on one and one quarter on the other

What your child learns in P3 fractions

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

Follows the latest (2026) MOE syllabus
See the syllabus wording
  • equivalent fractions
  • expressing a fraction in its simplest form
  • comparing and ordering unlike fractions with denominators of given fractions not exceeding 12
  • writing the equivalent fraction of a fraction given the denominator or the numerator
  • adding and subtracting two related fractions within one whole with denominators of given fractions not exceeding 12

Equivalent fractions

Equivalent fractions name the same amount: 1/3, 2/6 and 4/12 are one share, cut finer. Multiply or divide the numerator and the denominator by the same number. Your child also fills in a missing one, as in 2/3 = ?/12.

One third is two sixths and four twelfths

Simplest form

Divide the numerator and the denominator by the same number until nothing bigger than 1 divides both. 6/10 becomes 3/5. The pieces get bigger, the amount stays the same.

Six tenths in simplest form is three fifths

Comparing and ordering

Make one part match first. Same denominator: compare the numerators. Same numerator: the bigger denominator is the smaller fraction. Otherwise change one fraction, so 2/3 against 5/6 becomes 4/6 against 5/6.

Five sixths is more: 5 sixths against 4

Adding and subtracting

The denominators are related, like fifths and tenths. Change one fraction so the pieces match, then add or subtract the numerators only: 2/5 − 1/10 = 4/10 − 1/10 = 3/10. The answer stays within one whole.

Two fifths is four tenths; take away one, three tenths

Key facts and formulas

Term 3
  • Equivalent fractionsMultiply the numerator and the denominator by the same number. The fraction stays the same size.12=\frac{1}{2} = 1×22×2=\frac{1 \times 2}{2 \times 2} = 24\frac{2}{4}12=\frac{1}{2} = 1×42×4=\frac{1 \times 4}{2 \times 4} = 48\frac{4}{8}
  • Simplest formDivide the numerator and the denominator by the same number. Stop when no number divides both.69=\frac{6}{9} = 6÷39÷3=\frac{6 \div 3}{9 \div 3} = 23\frac{2}{3}
  • The missing numberWhat was the denominator multiplied by? Do the same to the numerator.denominator → 4×3=4 \times 3 = 121234=\frac{3}{4} = 3×34×3=\frac{3 \times 3}{4 \times 3} = 912\frac{9}{12}
  • Compare fractionsMake the denominators the same. The bigger numerator is the bigger fraction.23=\frac{2}{3} = 812\frac{8}{12}34=\frac{3}{4} = 912\frac{9}{12}
  • Add related fractionsMake the denominators the same, then add the numerators.12+14=\frac{1}{2} + \frac{1}{4} = 24+14=\frac{2}{4} + \frac{1}{4} = 34\frac{3}{4}
  • Subtract related fractionsMake the denominators the same, then subtract the numerators. Simplify if you can.56−13=\frac{5}{6} - \frac{1}{3} = 56−26=\frac{5}{6} - \frac{2}{6} = 36\frac{3}{6}36=\frac{3}{6} = 12\frac{1}{2}

Words to know

Numerator
The top number. It says how many pieces are taken.
Denominator
The bottom number. It says how many equal pieces the whole is cut into.
The whole
The one thing being shared. Two fractions compare fairly only on wholes the same size.
Equal parts
Pieces that are all the same size. A fraction only works on equal parts.

The sentence that costs the mark

Which is bigger, 13\frac{1}{3} or 14\frac{1}{4}?

What the working usually does

bigger bottom13\frac{1}{3} or 14\frac{1}{4}=14\frac{1}{4}

Picks 1/4 because 4 is bigger than 3. That is how whole numbers work, so it feels safe.

What the question asked

bigger piece13\frac{1}{3} or 14\frac{1}{4}=13\frac{1}{3}

Picks 1/3 because thirds are bigger pieces. The same whole cut into fewer parts leaves each part larger.

4 really is bigger than 3, so the slip passes unnoticed. But cut one bar into 3 and another into 4, and the thirds are plainly the wider pieces. The denominator counts the pieces, and more pieces means each one is smaller.

The same P3 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.

Put these fractions in order, starting from the smallest.

35\frac{3}{5}38\frac{3}{8}34\frac{3}{4}
Step 1 of 4▌
  1. All three fractions have the numerator 3. So we compare them by the size of their pieces.
  2. 8 is the biggest denominator, but eighths are the smallest pieces. The more pieces a whole is cut into, the smaller each piece is.
  3. Eighths are smaller than fifths, and fifths are smaller than quarters. So the order is 38\frac{3}{8}, 35\frac{3}{5}, 34\frac{3}{4}.
  4. So from the smallest, the order is 38\frac{3}{8}, 35\frac{3}{5}, 34\frac{3}{4}.

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

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Three quick P3 fractions questions

Try them together, then tap to check.

Question 1

What number goes in the box? 34=9□\frac{3}{4} = \frac{9}{\square}

Show answer

Answer12. The numerator 3 became 9, so it was multiplied by 3. Multiply the denominator by 3 too, 4 × 3 = 12.

Question 2

Write 48\frac{4}{8} in its simplest form.

Show answer

Answer12\frac{1}{2}. Divide the numerator and the denominator by 4: 4 ÷ 4 = 1 and 8 ÷ 4 = 2.

Question 3

Calculate 34+18\frac{3}{4} + \frac{1}{8}.

Show answer

Answer78\frac{7}{8}. Change 34\frac{3}{4} to 68\frac{6}{8} so the pieces match, then add the numerators: 6 + 1 = 7.

Helping at home

How to tell it has clicked

Ask which is bigger, 1/3 or 1/4. If the answer is 1/4 straight away, that is the slip. If your child stops to picture the pieces first, they have it.

For equivalent fractions, watch both numbers. A child who changes the top and leaves the bottom alone has changed the amount, not just how it is written.

Try this tonight

Share a chocolate bar between 3 people, then imagine sharing it between 4. More people, smaller share each. The denominator is the number of people.

Fold a strip of paper in half, then in half again. The same half now shows as 2 quarters. Same amount, more pieces.

Before and after P3 fractions

  1. Builds on

    Primary 2 Fractions

    Names equal parts of a whole

  2. You are here

    Primary 3 Fractions

    Compares, simplifies, adds and subtracts fractions

  3. Leads to

    Primary 4 Decimals

    Compares decimals place by place

  4. Leads to

    Primary 4 Fractions

    Adds fractions once the pieces match

  5. Leads to

    Primary 4 Pie Charts

    Reads each sector as a share

More in Primary 3

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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