Covers Lessons 6–10: Understanding, simplifying, adding, subtracting, multiplying and dividing fractions.
Question 9 3 marks
(a) Simplify $\frac{18}{24}$ to lowest terms. 1 mark
(b) Find the missing numerator: $\frac{3}{5} = \frac{?}{20}$ 1 mark
(c) Which is larger: $\frac{3}{4}$ or $\frac{5}{6}$? Show your working. 1 mark
(a) $\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}$ [1]
(b) $\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}$, so the missing numerator is $12$ [1]
(c) $\frac{3}{4} = \frac{9}{12}$ and $\frac{5}{6} = \frac{10}{12}$. Since $\frac{10}{12} > \frac{9}{12}$, $\frac{5}{6}$ is larger [1]
Question 10 3 marks
A recipe requires $\frac{2}{3}$ of a cup of flour. How much flour is needed for $3\frac{1}{2}$ batches? Give your answer as a mixed number.
Flour needed = $\frac{2}{3} \times 3\frac{1}{2} = \frac{2}{3} \times \frac{7}{2}$ [1]
$= \frac{2 \times 7}{3 \times 2} = \frac{14}{6}$ [1]
$= \frac{7}{3} = 2\frac{1}{3}$ cups [1]
Final answer: $2\frac{1}{3}$ cups
Question 11 4 marks
(a) Evaluate: $\frac{3}{4} + \frac{5}{6}$ 2 marks
(b) Evaluate: $2\frac{1}{2} \div \frac{5}{8}$ 2 marks
(a) LCD of 4 and 6 is 12. $\frac{3}{4} = \frac{9}{12}$ and $\frac{5}{6} = \frac{10}{12}$ [1]
$\frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12}$ [1]
(b) $2\frac{1}{2} \div \frac{5}{8} = \frac{5}{2} \div \frac{5}{8} = \frac{5}{2} \times \frac{8}{5}$ [1]
$= \frac{5 \times 8}{2 \times 5} = \frac{40}{10} = 4$ [1]
Final answers: (a) $1\frac{7}{12}$ (b) $4$