a) 2 5 × 9 8 \frac{2}{5}\times \frac{9}{8} 5 2 × 8 9 = 2 1 × 9 5 × 8 4 = 1 × 9 5 × 4 = 9 20 \frac{\overset{1}{\cancel{2}}\times 9}{5\times \underset{4}{\cancel{8}}}=\frac{1\times 9}{5\times 4}=\frac{9}{20} 5 × 4 8 2 1 × 9 = 5 × 4 1 × 9 = 20 9
10 7 × 21 20 \frac{10}{7}\times \frac{21}{20} 7 10 × 20 21 = 10 1 × 21 3 7 1 × 20 2 = 1 × 3 1 × 2 = 3 2 \frac{\overset{1}{\cancel{10}}\ \times \overset{3}{\cancel{21}}}{\underset{1}{\cancel{7}}\times \underset{2}{\cancel{20}}}=\frac{1\times 3}{1\times 2}=\frac{3}{2} 1 7 × 2 20 10 1 × 21 3 = 1 × 2 1 × 3 = 2 3
6 × 3 4 \ 6\times \frac{3}{4} 6 × 4 3 = 6 3 × 3 1 × 4 2 = 3 × 3 1 × 2 = 9 2 \frac{\overset{3}{\cancel{6}}\times 3}{1\times \underset{2}{\cancel{4}}}=\frac{3\times 3}{1\times 2}=\frac{9}{2} 1 × 2 4 6 3 × 3 = 1 × 2 3 × 3 = 2 9
9 10 × 7 3 × 5 14 \frac{9}{10}\times \frac{7}{3}\times \frac{5}{14} 10 9 × 3 7 × 14 5 = 9 3 × 7 1 × 5 1 10 2 × 3 1 × 14 2 = 3 × 1 × 1 2 × 1 × 2 = 3 4 \frac{\overset{3}{\cancel{9}}\times \overset{1}{\cancel{7}}\times \overset{1}{\cancel{5}}}{\underset{2}{\cancel{10}}\times \underset{1}{\cancel{3}}\times \underset{2}{\cancel{14}}}=\frac{3\times 1\times 1}{2\times 1\times 2}=\frac{3}{4} 2 10 × 1 3 × 2 14 9 3 × 7 1 × 5 1 = 2 × 1 × 2 3 × 1 × 1 = 4 3
b) 6 5 : 9 20 \frac{6}{5}:\frac{9}{20} 5 6 : 20 9 = 6 5 × 20 9 = 6 2 × 20 4 5 1 × 9 3 = 2 × 4 1 × 3 = 8 3 =\frac{6}{5}\times \frac{20}{9}=\frac{\overset{2}{\cancel{6}}\ \times \ \overset{4}{\cancel{20}}}{\underset{1}{\cancel{5}}\times \underset{3}{\cancel{9}}}=\frac{2\times 4}{1\times 3}=\frac{8}{3} = 5 6 × 9 20 = 1 5 × 3 9 6 2 × 20 4 = 1 × 3 2 × 4 = 3 8
8 : 16 5 8:\frac{16}{5} 8 : 5 16 = 8 × 5 16 = 8 1 × 5 1 × 16 2 = 1 × 5 1 × 2 = 5 2 =8\times \frac{5}{16}=\frac{\overset{1}{\cancel{8}}\times 5}{1\times \underset{2}{\cancel{16}}}=\frac{1\times 5}{1\times 2}=\frac{5}{2} = 8 × 16 5 = 1 × 2 16 8 1 × 5 = 1 × 2 1 × 5 = 2 5
21 4 : 7 \frac{21}{4}:7 4 21 : 7 = 21 4 × 1 7 = 21 3 × 1 4 × 7 1 = 3 × 1 4 × 1 = 3 4 =\frac{21}{4}\times \frac{1}{7}=\frac{\overset{3}{\cancel{21}}\times 1}{4\times \underset{1}{\cancel{7}}}=\frac{3\times 1}{4\times 1}=\frac{3}{4} = 4 21 × 7 1 = 4 × 1 7 21 3 × 1 = 4 × 1 3 × 1 = 4 3
6 × 1 12 : 5 2 6\times \frac{1}{12}:\frac{5}{2} 6 × 12 1 : 2 5 =6 × 1 12 × 2 5 = 6 1 × 1 × 2 1 1 × 12 1 × 5 = 1 × 1 × 1 1 × 1 × 5 = 1 5 6\times \frac{1}{12}\times \frac{2}{5}=\frac{\overset{1}{\cancel{6}\ }\times 1\times \overset{1}{\cancel{2}}}{1\times \underset{1}{\cancel{12}}\times 5}=\frac{1\times 1\times 1}{1\times 1\times 5}=\frac{1}{5} 6 × 12 1 × 5 2 = 1 × 1 12 × 5 6 1 × 1 × 2 1 = 1 × 1 × 5 1 × 1 × 1 = 5 1