1. **Work out the multiplications and simplify each:** **a.** $\frac{3}{5} \times \frac{6}{7}$ - Cancel common factors: $\frac{3}{\cancel{5}} \times \frac{\cancel{6}}{7} = \frac{3}{1} \times \frac{6}{7}$ - Actually, 3 and 6 share a factor 3: $\frac{\cancel{3}}{5} \times \frac{\cancel{6}}{7} = \frac{1}{5} \times \frac{2}{7}$ - Multiply: $\frac{1 \times 2}{5 \times 7} = \frac{2}{35}$ **b.** $\frac{4}{5} \times \frac{7}{12}$ - Cancel common factors: 4 and 12 share 4: $\frac{\cancel{4}}{5} \times \frac{7}{\cancel{12}} = \frac{1}{5} \times \frac{7}{3}$ - Multiply: $\frac{1 \times 7}{5 \times 3} = \frac{7}{15}$ **c.** $\frac{5}{6} \times \frac{7}{8}$ - No common factors to cancel. - Multiply: $\frac{5 \times 7}{6 \times 8} = \frac{35}{48}$ **d.** $\frac{19}{20} \times \frac{5}{6}$ - Cancel common factors: 5 and 20 share 5: $\frac{19}{\cancel{20}} \times \frac{\cancel{5}}{6} = \frac{19}{4} \times \frac{1}{6}$ - Multiply: $\frac{19 \times 1}{4 \times 6} = \frac{19}{24}$ **f.** $\frac{3}{4} \times \frac{12}{13}$ - Cancel common factors: 3 and 12 share 3: $\frac{\cancel{3}}{4} \times \frac{\cancel{12}}{13} = \frac{1}{4} \times \frac{4}{13}$ - Cancel 4 and 4: $\frac{1}{\cancel{4}} \times \frac{\cancel{4}}{13} = \frac{1}{1} \times \frac{1}{13} = \frac{1}{13}$ **g.** $\frac{6}{21} \times \frac{7}{18}$ - Cancel common factors: 6 and 18 share 6, 7 and 21 share 7: $\frac{\cancel{6}}{\cancel{21}} \times \frac{\cancel{7}}{\cancel{18}} = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$ **h.** $\frac{3}{8} \times \frac{8}{15}$ - Cancel common factors: 8 and 8 cancel: $\frac{3}{\cancel{8}} \times \frac{\cancel{8}}{15} = \frac{3}{1} \times \frac{1}{15} = \frac{3}{15} = \frac{1}{5}$ **i.** $\frac{21}{22} \times \frac{4}{6}$ - Cancel common factors: 21 and 6 share 3, 4 and 22 share 2: $\frac{\cancel{21}}{22} \times \frac{4}{\cancel{6}} = \frac{7}{22} \times \frac{4}{2} = \frac{7}{22} \times \frac{2}{1}$ - Cancel 2 and 22: $\frac{7}{\cancel{22}} \times \frac{\cancel{2}}{1} = \frac{7}{11} \times 1 = \frac{7}{11}$ 2. **Fraction of cakes Yasmina eats:** - Guests eat $\frac{3}{4}$ of cakes, so left is $1 - \frac{3}{4} = \frac{1}{4}$ - Yasmina eats $\frac{1}{4}$ of what is left: $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$ 3. **Fraction of salad Marie eats:** - Guests eat $\frac{9}{10}$ of salad, so left is $1 - \frac{9}{10} = \frac{1}{10}$ - Marie eats $\frac{2}{3}$ of what is left: $\frac{2}{3} \times \frac{1}{10} = \frac{2}{30} = \frac{1}{15}$