Fractions, Decimals and Percentages — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Divide the numerator by the denominator: 3 ÷ 8.

0.375

(b)Multiply the decimal by 100.

37.5%

Question 2

(a)Let x = 0.444… Then 10x = 4.444…, so 10x − x = 4.444… − 0.444… = 4, giving 9x = 4.

x = 4/9

Question 3

(a)Use the common denominator 12: 2/3 = 8/12 and 1/4 = 3/12, then add.

8/12 + 3/12 = 11/12

Question 4

(a)Divide 5 by 6.

0.833 (3 s.f.)

(b)Multiply the decimal by 100.

83.3%

Question 5

(a)This is a well-known recurring decimal equal to two-thirds.

2/3

Question 6

(a)Common denominator 20: 3/5=12/20, 1/4=5/20.

12/20 − 5/20 = 7/20

Question 7

(a)'Of' means multiply the fractions.

(1×5)/(3×7) = 5/21

Question 8

(a)Convert all to decimals for comparison: 0.7, 0.75, 0.65.

65%, 0.7, 3/4

Question 9

(a)Convert to improper fractions: 5/2 × 4/3 = 20/6 = 10/3.

10/3 = 3 1/3

Question 10

(a)0.375 = 375/1000; divide top and bottom by their HCF (125).

3/8

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