Practise Fractions and mixed numbers. 2 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy3 marks
Ben works out \(\frac{2}{3} + \frac{1}{4}\). His answer is \(\frac{3}{7}\).
(a) Without working out the correct answer, explain how you can tell that Ben's answer must be wrong.[1]
(b) Work out the correct answer.[2]
Show the answer and mark scheme
(a)Answer: \(\frac{3}{7}\) is less than \(\frac{2}{3}\), but adding \(\frac{1}{4}\) to \(\frac{2}{3}\) must give more than \(\frac{2}{3}\).
C1 for a correct reason, e.g. \(\frac{3}{7}\) is smaller than \(\frac{2}{3}\) (or smaller than \(\frac{1}{2}\)), but the answer must be bigger than \(\frac{2}{3}\)
Worked solution: Adding a positive number makes a number bigger, so the answer must be more than \(\frac{2}{3}\). But \(\frac{3}{7}\) is less than \(\frac{1}{2}\).
(b)Answer: \(\frac{11}{12}\)
M1 for a correct common denominator, e.g. \(\frac{8}{12} + \frac{3}{12}\)
A water tank is \(\frac{3}{5}\) full. After 42 litres of water are used, the tank is \(\frac{1}{4}\) full.
(a) Work out the capacity of the tank.[3]
(b) The tank is then filled until it is \(\frac{5}{6}\) full. How many litres of water are added?[2]
Show the answer and mark scheme
(a)Answer: 120 litres
P1 for \(\frac{3}{5} - \frac{1}{4} = \frac{7}{20}\)
P1 for \(42 \div \frac{7}{20}\) or \(42 \div 7 \times 20\)
A1 for 120
Worked solution: \(\frac{3}{5} - \frac{1}{4} = \frac{12}{20} - \frac{5}{20} = \frac{7}{20}\) of the tank is 42 litres. \(\frac{1}{20}\) is 6 litres, so the capacity is \(20 \times 6 = 120\) litres.
(b)Answer: 70 litres
M1 for \(\frac{5}{6} \times 120\) (= 100) or \(\frac{5}{6} - \frac{1}{4} = \frac{7}{12}\) (ft their capacity)
A1 for 70 (ft)
Worked solution: Now the tank holds \(\frac{1}{4} \times 120 = 30\) litres. \(\frac{5}{6} \times 120 = 100\) litres, so \(100 - 30 = 70\) litres are added.
Question 3Hard5 marks
The length of a rectangle is \(2\frac{1}{2}\) times its width. The area of the rectangle is \(15\frac{5}{8}\) cm2. Work out the perimeter of the rectangle. Give your answer as a mixed number in its simplest form.[5]
Show the answer and mark scheme
Answer: \(17\frac{1}{2}\) cm
P1 for dividing the area by \(2\frac{1}{2}\), e.g. \(\frac{125}{8} \times \frac{2}{5}\)
P1 for finding that the square of the width is \(\frac{25}{4}\)
P1 for the width, \(\frac{5}{2}\), and the length, \(6\frac{1}{4}\)
P1 for a complete method for the perimeter, e.g. \(2 \times \left(\frac{25}{4} + \frac{5}{2}\right)\)