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- multiplying and dividing fractions

multiplying fractions

example 1

example 2

$\tfrac{3}{4} \times \tfrac{5}{7} = \tfrac{15}{28}$

example 3

$\tfrac{2}{3} \times \tfrac{3}{4} = \tfrac{\cancel{2} ^{~1}}{\cancel{3} ^{~1}} \times \tfrac{\cancel{3} ^{~1}}{\cancel{4} ^{~2}} = \tfrac{1}{1} \times \tfrac{1}{2} = \tfrac{1}{2}$

example 4

$6 \times \tfrac{3}{4} = \tfrac{6}{1} \times \tfrac{3}{4} = \tfrac{18}{4}$

dividing two fractions

$\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$

examle

$\tfrac{1}{2} \div \tfrac{3}{4} = \tfrac{1}{2} \times \tfrac{4}{3} = \tfrac{1 \cdot 4}{2 \cdot 3} = \tfrac{2}{3}$ .

$\frac{\tfrac{3}{2}}5=\tfrac{3}{2}\times\tfrac{1}{5}=\tfrac{3}{10}.$

$\frac{8}{\tfrac{1}{3}}=8\times\tfrac{3}{1}=24.$

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