Fractions — P5 Mathematics

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Instructions: This worksheet has 2 sections. Answer all questions. Show all working. Express your answers as fractions in their simplest form or as mixed numbers where appropriate. Total: 15 questions.

Key Concepts Covered

Fraction of a quantity (part-whole)
Adding and subtracting fractions with different denominators
Multiplying fractions by whole numbers, fractions, and mixed numbers
Dividing fractions by whole numbers and vice versa
Fraction word problems (comparison, remainder, ratio)

Section A

Foundation

~10 min

Express your answers as fractions in their simplest form or as mixed numbers.

Find each of the following:

(a) 3/4 of 20 = ___
(b) 5/6 of 36 = ___
(c) 7/10 of 50 kg = ___ kg
(d) 2/3 of $48 = $___
(e) 9/20 of 160 ml = ___ ml

Simplify:

(a) 1/3 + 1/4 = ___
(b) 2/5 + 3/10 = ___
(c) 3/8 + 1/6 = ___
(d) 5/12 + 7/15 = ___
(e) 2/3 + 3/4 + 1/6 = ___

Simplify:

(a) 3/4 - 1/2 = ___
(b) 5/6 - 1/3 = ___
(c) 7/8 - 1/4 = ___
(d) 9/10 - 2/5 = ___
(e) 11/12 - 5/6 = ___

Simplify:

(a) 2/3 × 6 = ___
(b) 5/8 × 4 = ___
(c) 3/4 × 2/3 = ___
(d) 7/10 × 5/14 = ___
(e) 1 1/2 × 4/5 = ___

Simplify:

(a) 3/4 ÷ 2 = ___
(b) 5/6 ÷ 10 = ___
(c) 8 ÷ 2/3 = ___
(d) 12 ÷ 3/4 = ___
(e) 1 1/2 ÷ 3/5 = ___

Section B

Word Problems

~20 min

Show all your working. Express answers as fractions in their simplest form or as mixed numbers.

A box contains 240 marbles. 3/8 of the marbles are red and 1/4 of them are blue.

(a) How many marbles are red?
(b) How many marbles are blue?
(c) What fraction of the marbles are neither red nor blue? Express your answer in its simplest form.

Sarah has a ribbon that is 4 m long. She uses 3/5 of it to make decorations and gives the rest equally to her 2 friends.

(a) How much ribbon does Sarah use for decorations?
(b) How much ribbon does each friend receive?

A tank contains 60 litres of water. John uses 2/3 of the water to wash his car and then uses 1/4 of the remaining water to water his plants.

(a) How much water does he use to wash his car?
(b) How much water is left after washing the car?
(c) How much water does he use to water his plants?
(d) What fraction of the original amount of water is left? Express your answer in its simplest form.

Amy and Ben share a bag of sweets. Amy takes 3/7 of the sweets and Ben takes 2/5 of them.

(a) Who took more sweets?
(b) What fraction of the sweets is left? Express your answer in its simplest form.
(c) If there were 70 sweets in total, how many are left?

A recipe for cake requires 3/4 kg of flour. To make half the amount, how much flour is needed?

A rope is 9 m long. Tom cuts off 2/3 of it and then gives 3/4 of the remaining piece to his friend.

(a) How much rope does Tom cut off?
(b) How much rope is left after cutting?
(c) How much rope does his friend receive?
(d) What fraction of the original length does Tom keep? Express your answer in its simplest form.

Lily has $120. She spends 3/5 of her money on a dress and 1/4 of the remaining money on shoes.

(a) How much does she spend on the dress?
(b) How much money is left after buying the dress?
(c) How much does she spend on shoes?
(d) What fraction of her original money does she have left? Express your answer in its simplest form.

A movie lasts for 2 hours. During the movie, 1/4 of the time is action scenes and 3/8 of the time is comedy scenes.

(a) How many minutes are spent on action scenes?
(b) How many minutes are spent on comedy scenes?
(c) What fraction of the movie is neither action nor comedy? Express your answer in its simplest form.

A piece of cloth is 5 1/2 m long. It is cut into pieces that are each 3/4 m long.

(a) How many complete pieces can be cut?
(b) What fraction of a piece is left over? Express your answer in its simplest form.

A school has 480 students. 2/3 of the students are in Primary 4 to Primary 6. Of these, 3/5 are girls.

(a) How many students are in Primary 4 to Primary 6?
(b) How many of them are girls?
(c) What fraction of the total school population are P4-P6 girls? Express your answer in its simplest form.
(d) If the rest of the students (P1-P3) have an equal number of boys and girls, how many girls are there in the whole school?

Answer Key

Section A: Foundation

Q1.

(a) 3/4 × 20 = 15
(b) 5/6 × 36 = 30
(c) 7/10 × 50 = 35 kg
(d) 2/3 × $48 = $32
(e) 9/20 × 160 = 72 ml

Q2.

(a) 4/12 + 3/12 = 7/12
(b) 4/10 + 3/10 = 7/10
(c) 9/24 + 4/24 = 13/24
(d) 25/60 + 28/60 = 53/60
(e) 8/12 + 9/12 + 2/12 = 19/12 = 1 7/12

Q3.

(a) 3/4 - 2/4 = 1/4
(b) 5/6 - 2/6 = 3/6 = 1/2
(c) 7/8 - 2/8 = 5/8
(d) 9/10 - 4/10 = 5/10 = 1/2
(e) 11/12 - 10/12 = 1/12

Q4.

(a) 2/3 × 6 = 12/3 = 4
(b) 5/8 × 4 = 20/8 = 5/2 = 2 1/2
(c) 3/4 × 2/3 = 6/12 = 1/2
(d) 7/10 × 5/14 = 35/140 = 1/4
(e) 3/2 × 4/5 = 12/10 = 6/5 = 1 1/5

Q5.

(a) 3/4 ÷ 2 = 3/8
(b) 5/6 ÷ 10 = 5/60 = 1/12
(c) 8 × 3/2 = 24/2 = 12
(d) 12 × 4/3 = 48/3 = 16
(e) 3/2 × 5/3 = 15/6 = 5/2 = 2 1/2

Section B: Word Problems

Q6.

(a) 3/8 × 240 = 90 marbles are red
(b) 1/4 × 240 = 60 marbles are blue
(c) Red + Blue = 3/8 + 1/4 = 3/8 + 2/8 = 5/8. Left = 1 - 5/8 = 3/8

Q7.

(a) 3/5 × 4 m = 12/5 m = 2 2/5 m (or 2.4 m)
(b) Remaining: 4 - 2 2/5 = 1 3/5 m. Each friend: 1 3/5 ÷ 2 = 8/5 × 1/2 = 8/10 = 4/5 m

Q8.

(a) 2/3 × 60 = 40 litres
(b) 60 - 40 = 20 litres
(c) 1/4 × 20 = 5 litres
(d) Left: 20 - 5 = 15 L. Fraction: 15/60 = 1/4

Q9.

(a) Amy: 3/7 = 15/35. Ben: 2/5 = 14/35. Amy took more (15/35 > 14/35)
(b) Taken: 15/35 + 14/35 = 29/35. Left: 1 - 29/35 = 6/35
(c) 6/35 × 70 = 12 sweets

Q10.

3/4 × 1/2 = 3/8 kg. Answer: 3/8 kg

Q11.

(a) 2/3 × 9 = 6 m
(b) 9 - 6 = 3 m
(c) 3/4 × 3 = 9/4 = 2 1/4 m
(d) Tom keeps: 3 - 2 1/4 = 1/4 m. Fraction of original: (1/4)/9 = 1/36

Q12.

(a) 3/5 × $120 = $72
(b) $120 - $72 = $48
(c) 1/4 × $48 = $12
(d) Left: $48 - $12 = $36. Fraction: 36/120 = 3/10

Q13.

(a) 1/4 × 120 min = 30 minutes
(b) 3/8 × 120 min = 45 minutes
(c) Action + Comedy: 1/4 + 3/8 = 2/8 + 3/8 = 5/8. Left: 1 - 5/8 = 3/8

Q14.

(a) 5 1/2 ÷ 3/4 = 11/2 × 4/3 = 44/6 = 7 remainder 2/6. Answer: 7 complete pieces
(b) Leftover: 11/2 - 7×3/4 = 11/2 - 21/4 = 22/4 - 21/4 = 1/4 m. Fraction of a piece: (1/4)/(3/4) = 1/3

Q15.

(a) 2/3 × 480 = 320 students
(b) 3/5 × 320 = 192 girls
(c) 192/480 = 2/5
(d) P1-P3: 480 - 320 = 160 students. Half are girls: 160 ÷ 2 = 80. Total girls: 192 + 80 = 272 girls