Covers Lessons 11–15: Decimals, conversions, percentages, financial mathematics and ratios.
Question 9 3 marks
(a) Convert 0.625 to a fraction in lowest terms. 1 mark
(b) Convert 3/8 to a decimal. 1 mark
(c) Convert 0.08 to a percentage. 1 mark
(a) $0.625 = \frac{625}{1000} = \frac{5}{8}$ [1]
(b) $\frac{3}{8} = 3 \div 8 = 0.375$ [1]
(c) $0.08 \times 100 = 8\%$ [1]
Question 10 3 marks
A shop buys headphones for $40 and wants to make a 30% profit.
(a) What is the profit amount? 1 mark
(b) What should the selling price be? 1 mark
(c) If the shop then offers a 10% discount on the selling price, what does the customer pay? 1 mark
(a) Profit = $30\%$ of $\$40 = 0.30 \times 40 = \$12$ [1]
(b) Selling price = $\$40 + \$12 = \$52$ [1]
(c) Discount = $10\%$ of $\$52 = \$5.20$. Customer pays $\$52 - \$5.20 = \$46.80$ [1]
Question 11 4 marks
The ratio of red to blue marbles in a bag is 2:5.
(a) If there are 14 red marbles, how many blue marbles are there? 2 marks
(b) How many marbles are in the bag altogether? 1 mark
(c) What fraction of the marbles are blue? 1 mark
(a) 2 parts = 14 marbles, so 1 part = 7 marbles [1]. Blue = 5 parts = $5 \times 7 = 35$ marbles [1]
(b) Total = $14 + 35 = 49$ marbles [1]
(c) Fraction blue = $\frac{5}{2+5} = \frac{5}{7}$ [1]