4MA1/2FR Jan 2019, Question 3: Multiplication and Division of Fractions

Part (a) · 1 mark

Shade 3/7 of a rectangle shown split into 21 equal squares.

1. 1The rectangle is divided into 7 columns and 3 rows
2. 2Total number of squares = 7 × 3 = 21
3. 33/7 of 21 = 21 ÷ 7 × 3
4. 421 ÷ 7 = 3
5. 53 × 3 = 9
6. 6Shade any 9 of the 21 squares

Answer9 squares shaded (any 9 of the 21 squares)

Part (b) · 1 mark

Express 23/3 as a mixed number.

1. 123/3 means 23 ÷ 3
2. 223 ÷ 3 = 7 remainder 2
3. 3The 7 is the whole number part and the remainder 2 goes over the denominator 3
4. 423/3 = 7 2/3

Answer7 2/3

Part (c) · 2 marks

Work out 2/5 of 60 cm.

1. 12/5 of 60 cm = 60 ÷ 5 × 2
2. 260 ÷ 5 = 12
3. 312 × 2 = 24
4. 42/5 of 60 cm = 24 cm

Answer24 cm

Part (d) · 2 marks

Decide if Claude is right that 1/6 is exactly halfway between 1/4 and 1/8, giving a reason.

1. 1Write all three fractions over a common denominator of 24
2. 21/4 = 6/24
3. 31/8 = 3/24
4. 41/6 = 4/24
5. 5Halfway between 3/24 and 6/24 is (3 + 6) ÷ 2 = 4.5, that is 4.5/24
6. 61/6 is 4/24, which is not 4.5/24
7. 7No, Claude is not correct — 1/6 is not exactly halfway between 1/4 and 1/8

AnswerNo, because 1/4 = 6/24 and 1/8 = 3/24, so halfway between them is 4.5/24, but 1/6 = 4/24

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