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Question Number 119814 by bemath last updated on 27/Oct/20

$$Ifa,b,canddisrealnumbers$$$$satisfy\frac{a}{b}=\frac{2}{3},\frac{c}{d}=\frac{4}{5},\frac{d}{b}=\frac{6}{7}$$$$then\frac{a}{c}=?$$

Answered by Olaf last updated on 27/Oct/20

$$a=\frac{2}{3}b$$$$c=\frac{4}{5}d=\frac{4}{5}\left(\frac{6}{7}b\right)=\frac{24}{35}b$$$$$$$$\frac{a}{c}=\frac{2}{3}b\times \frac{35}{24b}=\frac{35}{36}$$

Answered by talminator2856791 last updated on 27/Oct/20

$$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{\frac{bc}{d}}=\frac{ad}{bc}=\frac{\frac{2}{3}}{\frac{4}{5}}$$$$\frac{a}{c}=\frac{ad}{bc}\mathbf{÷}\frac{d}{b}=\frac{\frac{2}{3}}{\frac{4}{5}}\mathbf{÷}\frac{6}{7}=\frac{35}{36}$$

Answered by $@y@m last updated on 27/Oct/20

$$\frac{a}{c}=\frac{a}{b}\times \frac{b}{d}\times \frac{d}{c}=\frac{2}{3}\times \frac{7}{6}\times \frac{5}{4}=\frac{35}{36}$$

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