Primary 4 Fractions Study Guide

Primary 4 fractions in six short steps: what a fraction is, then mixed numbers, unlike fractions, a fraction of a set, a fraction of the remainder and finding the whole, with something to try at each step and worked examples to finish.

Start here

What is a fraction?

A fraction counts equal parts of one whole.

The denominator, at the bottom, says how many equal parts the whole is cut into. The numerator, at the top, says how many of those parts we have. In 3/4, the whole is cut into 4 equal parts and we have 3 of them.

In Primary 4 the whole changes, and the idea stays the same:

  • more parts than one whole holds make a mixed number;
  • parts can only be added when they are the same size;
  • the whole can be a set of things, such as 12 counters;
  • after something is used up, what is left becomes a new whole;
  • knowing a few parts lets you work back to the whole.
1

Step 1

Mixed numbers and improper fractions

Same amount, counted two ways. An improper fraction counts every part. A mixed number counts the full wholes first, then the parts left over. The denominator stays the same, because the size of one part does not change.

Tap a part, or use the buttons

Cut each whole into equal parts
Try it

Express 2 3/8 as an improper fraction.

▶ Watch the lesson: Mixed and improperPractise 18 questions →
2

Step 2

Adding and subtracting unlike fractions

Make the parts the same size first. Unlike fractions have different denominators, so their parts are different sizes. Cut every part into smaller equal parts until both fractions share one denominator. Then add or subtract the numerators.

Try it

Find the value of 3/4 + 1/6.

▶ Watch the lesson: Unlike fractionsPractise 7 questions →
3

Step 3

Finding a fraction of a set

The denominator makes the groups. To find a fraction of a set, share the whole set into as many equal groups as the denominator says. The numerator says how many groups to take.

Tap a fraction

Findof 12
Try it

What is 2/3 of 18?

▶ Watch the lesson: A fraction of a setPractise 3 questions →
4

Step 4

A fraction of the remainder

What is left becomes the new whole. When a question says "of the remainder", the second fraction is a fraction of what was left, not of the amount at the start. Cut the remainder into equal parts, then make every unit the same size.

Siti had $60. She spent 1/3 of her money on a book and 1/4 of the remainder on a pen. How much money did she have left?

Try it

Mrs Lim baked 40 cookies. She gave 1/4 of them to her neighbour and 1/2 of the remainder to her sister. How many cookies did her sister get?

▶ Watch the lesson: Fraction of the remainderPractise 9 questions →
5

Step 5

Finding the whole from a fraction

Find 1 unit, then the whole. Let the whole be as many units as the denominator. The number you are given is a count of units too. Divide to find 1 unit, then multiply to find the whole.

Try it

3/7 of the pupils in a hall are boys. There are 27 boys. How many pupils are there in the hall?

▶ Watch the lesson: Recover the wholePractise 6 questions →

Primary 4 fractions questions, worked step by stepTry each question first. Then show a hint, or the working one line at a time.

Mixed and improperBasic

Express 3 5/7 as an improper fraction.

Each whole is cut into 7 equal parts. How many parts are in 3 wholes? Then add the extra parts.
  1. 3 wholes have 3 × 7 = 21 parts.
  2. Add the 5 extra parts: 21 + 5 = 26.
  3. The denominator stays 7: 3 5/7 = 21/7 + 5/7 = 26/7
Answer: 26/7
Fraction of a setIntermediate

There are 36 pupils in a class. 4/9 of them wear spectacles. How many pupils do not wear spectacles?

Let the whole class be 9 units. If 4 units wear spectacles, how many units do not?
  1. Let the class be 9 units. Spectacles: 4 units. No spectacles: 9 − 4 = 5 units.
  2. 9 units = 36, so 1 unit = 36 ÷ 9 = 4.
  3. 5 units = 5 × 4 = 20.
  4. Check: 4 units = 16 wear spectacles, and 16 + 20 = 36.
Answer: 20 pupils
Unlike fractionsIntermediate

Mei Ling had 2 kg of flour. She used 3/4 kg of it for a cake and 1/6 kg for some biscuits. How much flour did she have left?

Add the two amounts she used first. The smallest common multiple of 4 and 6 is 12. To minus from 2, rename one whole as twelfths.
  1. Smallest common multiple of 4 and 6 = 12.
  2. Flour used = 3/4 + 1/6 = 9/12 + 2/12 = 11/12 kg
  3. Rename one whole: 2 = 1 12/12
  4. Flour left = 1 12/12 − 11/12 = 1 1/12 kg
Answer: 1 1/12 kg
Fraction of the remainderIntermediate

A baker made 96 tarts. She sold 3/8 of them in the morning and 2/5 of the remaining tarts in the afternoon. How many tarts were left?

Find how many tarts remained after the morning first. The 2/5 is of that remainder, not of 96.
  1. Let the tarts be 8 units. 1 unit = 96 ÷ 8 = 12, so the morning’s 3 units = 3 × 12 = 36 tarts sold.
  2. Remainder = 96 − 36 = 60 tarts.
  3. Afternoon: 60 ÷ 5 = 12, so 2/5 of 60 = 2 × 12 = 24 tarts sold.
  4. Tarts left = 60 − 24 = 36. Check: 36 + 24 + 36 = 96.
Answer: 36 tarts
Finding the wholeChallenge

Devi had some stickers. She gave 1/3 of them to Ali and 1/4 of the remainder to Ben. She had 24 stickers left. How many stickers did she have at first?

Draw a bar cut into 3 equal parts. The remainder is 2 parts; cut it into 4 equal units. Then make every unit the same size.
  1. Ali gets 1 of 3 parts. The remainder is 2 parts; cut it into 4 units, so each part is 2 units and the whole is 6 units.
  2. Ali = 2 units. Ben = 1 unit. Left = 4 − 1 = 3 units.
  3. 3 units = 24, so 1 unit = 24 ÷ 3 = 8.
  4. At first: 6 units = 6 × 8 = 48. Check: Ali 16, Ben 8, left 24, and 16 + 8 + 24 = 48.
Answer: 48 stickers
6

Step 6

Check yourself

Five quick questions, one from each step. Answers are not saved; they show where to practise next.

1. Express 17/5 as a mixed number.

2. Find the value of 5/6 − 1/4.

3. What is 2/7 of 35?

4. Ali had 30 stamps. He gave away 1/3 of them, then 1/2 of the remainder. How many stamps were left?

5. 2/5 of a number is 24. What is the number?

0/5
Answer all five to see where to practise next.
For parents

How to use this guide. Sit with your child for the first two steps. Before they tap, ask "How many parts make one whole?" and "Are the parts the same size?" Those two questions carry the whole chapter. Each step takes two or three minutes; the whole guide about fifteen.

In the word problems, ask your child to say what each fraction is a fraction of before they calculate: the whole set, or what is left. Then let them try a worked example first and reveal the working one line at a time.

More study guides

Before this: Tables and Line GraphsNext: AnglesPrimary 4 Numbers to 100 000 study guidePrimary 4 Factors and Multiples study guidePrimary 4 Four Operations of Whole Numbers study guide
Lessons and practice

P4 Fractions lessons and practice

5 lesson videos and 49 questions across five subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →