Primary 6 Fractions Study Guide
Primary 6 fractions in six short steps, from a fraction of a set to dividing by a fraction and the word problems built on them. Each step has a bar to cut, fold or share and a question to try.
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How do you divide fractions in Primary 6?
In Primary 6, every division turns into a multiplication.
Dividing by 2 is the same as multiplying by one half. Dividing by a fraction is the same as multiplying by its reciprocal, which is the fraction turned upside down. The word problems then ask the same question each time: which whole is this fraction of?
In this chapter, your child uses this to:
- find a fraction of a set by making equal groups;
- multiply two fractions, because "of" means multiply;
- share a fraction equally among a whole number of people;
- count how many equal fractions fit into a whole number;
- solve fraction of a remainder problems, equal fractions of two quantities, and a ratio read as a fraction.
Step 1
Fraction of a set
The bottom number makes the groups. Split the whole set into as many equal groups as the bottom number says. Every group is the same size. The top number says how many groups to take.
Pick a fraction, then follow the two steps
A box holds 30 eggs. 3/5 of the eggs are white. How many of the eggs are white?
Step 2
Multiplying fractions
A fraction of a fraction is a multiplication. Shade the first fraction, then fold the other way to take a fraction of it. Multiply the numerators, then multiply the denominators. Where a top and a bottom number share a factor, cancel across the times sign first.
Pick one, then fold the other way
Work out 2/3 × 3/5. Give your answer in its simplest form.
Step 3
Dividing a fraction by a whole number
Share it out by multiplying by one over the number. Dividing by 4 is the same as multiplying by one quarter. Cut every part into that many equal pieces and take one row. So the bottom number is multiplied by the whole number.
Pick a fraction, then share it out
3/4 of a pizza is shared equally among 3 friends. How much of the pizza does each friend get?
Step 4
Dividing a whole number by a fraction
Count how many fit, then turn the fraction upside down. To divide by a fraction, multiply by its reciprocal. 1/4 turned upside down is 4/1, which is 4. Dividing by a fraction smaller than 1 gives more than you started with.
Pick a jug, then pour it into cups
A ribbon 3 m long is cut into pieces of 3/8 m each. How many pieces are there?
Step 5
Fraction of the remainder word problems
Cut through the whole bar so every unit is the same size. The second fraction is taken from what was left, not from the amount at first. Split the remainder into the units it needs, and carry the cut across the bar. Then one unit leads to the amount at first.
Aiden had some stickers. He gave 1/3 of them to his brother. He then gave 2/5 of the remainder to his sister. He had 36 stickers left. How many stickers did he have at first?
Follow the four steps
Mei had some beads. She used 1/4 of them. Then she used 1/3 of the remainder. She had 42 beads left. How many beads did she have at first?
Step 6
Equal fractions of two quantities, and ratio
Equal fractions of two wholes are the same unit. If 1/3 of the boys is 1/5 of the girls, one unit is shared by both bars: the boys are 3 units and the girls are 5. Read the same bar as a ratio, 3 : 5, or as a fraction of all the children, 3/8. A fraction needs a whole, so add the units first.
In a hall, 1/3 of the boys is equal to 1/5 of the girls. There are 48 children in the hall altogether. How many boys are there?
Follow the four steps
The number of Adam's bottle caps to Grace's is in the ratio 3 : 5. What fraction of all the caps are Grace's?
Primary 6 fractions questions, worked step by stepWork each one on paper before you open anything. Then reveal the working a line at a time to check yours.
Find the value of 4/9 ÷ 6. Give your answer in its simplest form.
- 4
/9 ÷ 6 = 4/9 × 1/6 - Cancel 4 and 6 by 2: 2
/9 × 1/3 - = 2
/27
Mrs Lim has 6 kg of flour. She packs all of it into bags of 3/4 kg each. How many bags does she fill?
- Number of bags = 6 ÷ 3
/4 - = 6 × 4
/3 - Cancel 6 and 3 by 3: 2 × 4 = 8
There are 40 pupils in a class. 3/5 of them walk to school. 1/4 of the pupils who walk live in the same block of flats. How many pupils live in that block?
- 40 ÷ 5 = 8 pupils in each group
- Pupils who walk = 3 × 8 = 24
- Same block = 1
/4 × 24 = 6
At a carnival, 2/3 of the adults is equal to 1/2 of the children. There are 63 people at the carnival altogether. How many children are there?
- 2
/3 of the adults = 1/2 of the children = 2 units - Adults = 3 units, children = 4 units
- 7 units = 63, so 1 unit = 63 ÷ 7 = 9
- Children = 4 × 9 = 36
Farah had some money. She spent 1/4 of it on a dress and 2/3 of the remainder on a pair of shoes. She spent $20 more on the shoes than on the dress. How much money did she have at first?
- Dress = 1 unit, remainder = 4 units − 1 unit = 3 units
- Shoes = 2
/3 × 3 units = 2 units - Shoes − dress = 2 units − 1 unit = 1 unit = $20
- At first = 4 × $20 = $80
Step 7
Check yourself
Five questions on the Primary 6 skills. Nothing is recorded; each answer names the question type to look at again.
1. Work out 5/6 × 3/10.
2. Find 6/7 ÷ 3.
3. How many pieces of 1/3 m can be cut from a 5 m string?
4. Ravi had some marbles. He gave away 1/2 of them, then 1/3 of the remainder. He had 20 marbles left. How many marbles did he have at first?
5. 1/2 of Ali's stamps is equal to 1/4 of Ben's stamps. They have 90 stamps altogether. How many stamps does Ali have?
How to use this guide. Do Steps 1 and 2 first, even if your child met them in Primary 4 and 5: the later word problems lean on both. In Steps 3 and 4 ask your child, before they tap, whether the answer will be bigger or smaller than the number they started with. Sharing gives less; counting how many fit gives more.
For Steps 5 and 6, have your child copy each working line onto paper as it appears and say which whole the fraction is of. Then let them try the worked examples on their own and open the working only to compare, one line at a time.
More study guides
P6 Fractions lessons and practice
6 lesson videos and 47 questions across six subtopics, from Basic to Challenge, each with a worked solution.
Watch and practise →