Primary 3 Fractions Study Guide

Primary 3 fractions in four short steps, from equivalent fractions to adding related fractions. Each step has a bar to cut or group and a question to try.

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What are equivalent fractions?

Equivalent fractions name the same amount with different equal parts.

The bottom number, the denominator, shows how many equal parts make the whole. The top number, the numerator, counts the parts that are shaded. Cut every part into smaller equal parts and both numbers grow, yet the shaded amount does not change.

In this chapter, your child uses this to:

  • find a missing numerator or denominator by multiplying or dividing both numbers by the same number;
  • write a fraction in its simplest form, grouping parts until only 1 divides both numbers;
  • compare and order unlike fractions once the parts are the same size;
  • add or subtract related fractions, such as halves and eighths, within one whole.
1

Step 1

Finding equivalent fractions

Cut each part into the same number of pieces. The shaded part must stay the same, so the numerator and the denominator are both multiplied by that number. To go back, divide both by the same number.

Tap a fraction, then cut the parts

Fraction
Cut each part intopieces
2/3
2/3: the whole is cut into 3 equal parts and 2 of them are shaded. Cut each part into smaller pieces.
Try it

Complete the equivalent fraction: 2/3 = 8/?

▶ Watch the lesson: Equal and equivalent partsPractise 11 questions →
2

Step 2

Writing a fraction in its simplest form

Group the parts, then count the groups. Divide the numerator and the denominator by the same number. A group must be all shaded or all unshaded. Stop when only 1 divides both numbers.

Tap a group size

8/12
8/12: 8 of the 12 equal slices are shaded. Group the slices so every group is all shaded or all unshaded.
Try it

Write 8/10 in its simplest form.

▶ Watch the lesson: Simplest formPractise 10 questions →
3

Step 3

Comparing and ordering unlike fractions

To compare, we need parts of the same size. Unlike fractions have different denominators. Change one fraction so both have the same denominator, then compare the numerators. To order three fractions, change all of them into the same parts.

Pick a pair, then make the parts match

3/4 and 7/8 have different denominators, so their parts are different sizes. We cannot compare them yet.
Try it

Which is greater, 2/3 or 5/6?

▶ Watch the lesson: Compare unlike fractionsPractise 12 questions →
4

Step 4

Adding and subtracting related fractions

First make the parts the same size. Related fractions, such as halves and eighths, have one denominator that fits into the other. Cut the bigger parts to match. Then add or subtract the numerators, and keep the denominator.

Pick a sum, then follow the two steps

1/2 + 3/8: a half and an eighth are different sizes, so we cannot add the numerators yet.
Try it

Find 2/5 − 1/10. Give your answer in its simplest form.

▶ Watch the lesson: Add related fractionsPractise 8 questions →

Primary 3 fractions questions, worked step by stepHave a go on paper first. Reveal a hint, or the working line by line, only when you need it.

Equivalent fractionsBasic

Find the missing numbers. 3/4 = ?/8 = 9/?

Compare the denominators you know. What is 4 multiplied by to make 8? Then compare the numerators 3 and 9.
3/4 = 6/8 = 9/12. The missing numbers are 6 and 12.
Simplest formBasic

Siti cut a pizza into 12 equal slices. She ate 9 of the slices. What fraction of the pizza did she eat? Give your answer in its simplest form.

Write the slices she ate over the slices in all. Then find a number that divides both.
3/4 of the pizza
Comparing and orderingIntermediate

Arrange these fractions in order, beginning with the smallest. 1/2, 5/12, 2/3

Make the parts the same size. 2 and 3 both fit into 12, so write every fraction in twelfths.
5/12, 1/2, 2/3
Adding related fractionsIntermediate

Bala painted 3/10 of a fence on Monday and 2/5 of it on Tuesday. What fraction of the fence did he paint on the two days?

Fifths and tenths are related. Cut each fifth into 2 equal parts to make tenths.
7/10 of the fence
Adding and subtracting related fractionsChallenge

Mrs Tan baked a tray of kueh. She gave 1/4 of the tray to her neighbour and 3/8 of it to her sister. What fraction of the tray did she have left? Give your answer in its simplest form.

Find the fraction she gave away first. Then minus it from one whole, written in eighths.
3/8 of the tray
5

Step 5

Check yourself

Five short questions across the four steps. Nothing is saved; each answer simply points to the practice that fits.

1. Which fraction is equal to 3/4?

2. Write 4/10 in its simplest form.

3. Which is smaller, 5/6 or 7/12?

4. Which fraction is the greatest: 7/12, 3/4 or 2/3?

5. Find 7/10 − 1/5. Give your answer in its simplest form.

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

How to use this guide. Sit beside your child for Step 1 and let them do the tapping. Each time they cut the parts smaller, ask "Is the shaded part any bigger now?" The answer, no, is what every later step depends on. A step takes two or three minutes.

When your child compares, adds or subtracts, ask which fraction has the bigger parts and how to cut those parts to match the others. Then have them try a worked example on paper and reveal the working only to check each line.

More study guides

Before this: Perpendicular and Parallel LinesNext: Length, Mass and VolumePrimary 4 Fractions study guidePrimary 3 Angles study guidePrimary 3 Time study guidePrimary 3 More Word Problems study guide
Lessons and practice

P3 Fractions lessons and practice

4 lesson videos and 53 questions across four subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →