Fractions

Fractions are just pieces of a whole — a slice of pizza, a bit of a chocolate bar, part of your pocket money saved. The part most students trip over is that you cannot add fractions until the pieces are the same size. Cut everything into matching pieces first, and fractions become friendly. Let's slice into it.

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 add and subtract unlike fractions and mixed numbers, multiply fractions, find a fraction of a set, and link fractions to division. Here we go.

Adding and subtracting unlike fractions

Fractions with different bottoms are unlike fractions. You cannot add them straight away because the pieces are different sizes. First make the bottoms match using a common denominator.

To work out one half plus one third, the smallest common bottom is 6. One half becomes 3 sixths, one third becomes 2 sixths. Now add the tops: 3 + 2 = 5, giving five sixths. The bottom stays 6 because the piece size has not changed.

Adding and subtracting mixed numbers

A mixed number has a whole part and a fraction part. To add them, deal with the wholes and the fractions separately, then combine. Make the fraction bottoms match just like before.

Try two and one third plus one and one half. Add the wholes: 2 + 1 = 3. Add the fractions: one third plus one half is two sixths plus three sixths, which is five sixths. So the answer is three and five sixths.

Multiplying a fraction by a whole number

Multiplying a fraction by a whole number means adding that fraction several times. Three lots of two fifths is two fifths + two fifths + two fifths, which is six fifths. The shortcut: multiply the top by the whole number and keep the bottom the same.

So two fifths × 3 = (2 × 3) over 5 = six fifths, which as a mixed number is one and one fifth. Picture three bowls each holding two fifths of a litre of soup — together that is six fifths of a litre.

Multiplying a fraction by a fraction

To multiply two fractions, multiply the tops together and the bottoms together. One half of one third means one half × one third = (1 × 1) over (2 × 3) = one sixth. The word "of" between fractions always means multiply.

Think of half a strip of land, then a third of that half — you end up with one sixth of the whole strip. Multiplying makes the piece smaller, which feels strange at first but makes sense once you picture it.

Fraction of a set and relating to division

To find a fraction of a set, multiply the fraction by the total. Three quarters of 20 sweets is three quarters × 20 = 60 over 4 = 15 sweets. The bottom of the fraction tells you how many equal groups; the top tells you how many groups you take.

This is also why a fraction is just a division. The fraction three quarters means 3 ÷ 4. So three quarters of 20 is the same as (20 ÷ 4) × 3 = 5 × 3 = 15. Either route gives the same answer.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

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

1. What is one third plus one sixth?

   One halfTwo ninthsTwo sixths

2. What is two and one half plus one and one half?

   Three and one halfFourThree and two quarters

3. What is three sevenths multiplied by 2?

   Six seventhsThree fourteenthsFive sevenths

4. What is one half multiplied by two fifths?

   One fifthThree tenthsTwo sevenths

5. What is three quarters of 24 sweets?

   6188

6. A pizza is cut into 8 equal slices. You eat three eighths and your friend eats two eighths. What fraction is left?

   Three eighthsFive eighthsOne eighth

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