If-a-b-c-and-d-is-real-numbers-satisfy-a-b-2-3-c-d-4-5-d-b-6-7-then-a-c-

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

I f a, b, c a n d d i s r e a l n u m b e r s

s a t i s f y \frac{a}{b} = \frac{2}{3}, \frac{c}{d} = \frac{4}{5}, \frac{d}{b} = \frac{6}{7}

t h e n \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} (\frac{6}{7} b) = \frac{24}{35} b

\frac{a}{c} = \frac{2}{3} b \times \frac{35}{24 b} = \frac{35}{36}

Answered by talminator2856791 last updated on 27/Oct/20

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{\frac{b c}{d}} = \frac{a d}{b c} = \frac{\frac{2}{3}}{\frac{4}{5}}

\frac{a}{c} = \frac{a d}{b c} \div \frac{d}{b} = \frac{\frac{2}{3}}{\frac{4}{5}} \div \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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