1.17 Adding and subtracting fractions
9 exam questions worth 23 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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What is \frac{1}{2} + \frac{1}{3}?
Choose one answer.
Correct Not quite: the answer is \( \frac{5}{6} \)
Mark scheme
B: \frac{5}{6}
Model answer
\frac{5}{6} (B). 1/2 = 3/6 and 1/3 = 2/6, so the sum is 5/6.
Work out \dfrac{3}{8} + \dfrac{2}{5}.
Mark scheme
M1: common denominator 40 (15/40 and 16/40); A1: 31/40
Model answer
3/8 = 15/40 and 2/5 = 16/40. The sum is 31/40.
Work out \dfrac{5}{6} - \dfrac{3}{8}.
Mark scheme
M1: common denominator 24 (20/24 and 9/24); A1: 11/24
Model answer
5/6 = 20/24 and 3/8 = 9/24, so 20/24 - 9/24 = 11/24.
Work out \dfrac{3}{4} + \dfrac{5}{6}. Give your answer as a mixed number.
Mark scheme
M1: common denominator 12 (9/12 and 10/12); A1: 19/12; A1: 1 7/12
Model answer
3/4 = 9/12 and 5/6 = 10/12. The sum is 19/12 = 1 7/12.
Work out 2\dfrac{1}{3} + 1\dfrac{3}{4}.
Mark scheme
M1: adds whole numbers and fractions or converts to improper fractions (7/3 and 7/4); M1: common denominator 12; A1: 4 1/12
Model answer
2 + 1 = 3. 1/3 + 3/4 = 4/12 + 9/12 = 13/12 = 1 1/12. Total 4 1/12.
Work out 3\dfrac{1}{4} - 1\dfrac{2}{3}.
Mark scheme
M1: converts to improper fractions (13/4 and 5/3); M1: 39/12 - 20/12; A1: 1 7/12
Model answer
13/4 - 5/3 = 39/12 - 20/12 = 19/12 = 1 7/12.
Work out -\dfrac{1}{2} + \dfrac{1}{3}.
Mark scheme
M1: common denominator 6 (-3/6 + 2/6); A1: -1/6
Model answer
-3/6 + 2/6 = -1/6.
Sam eats \frac{1}{3} of a pizza and Tia eats \frac{1}{4} of the pizza. What fraction of the pizza is left?
Mark scheme
M1: 1/3 + 1/4 = 7/12; M1: 1 - 7/12; A1: 5/12
Model answer
Eaten: 4/12 + 3/12 = 7/12. Left: 12/12 - 7/12 = 5/12.
A tank has a capacity of 80 litres. It is \frac{3}{8} full. A further \frac{1}{4} of the tank's capacity is added and then \frac{1}{2} of its capacity is removed. How many litres are in the tank now?
Mark scheme
M1: 3/8 + 1/4 = 5/8; M1: 5/8 - 1/2 = 1/8; M1: 1/8 × 80; A1: 10 litres
Model answer
3/8 + 2/8 = 5/8. 5/8 - 4/8 = 1/8. 1/8 of 80 = 10 litres.
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