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Keith_Richards [23]
3 years ago
6

If x:y =a:b, prove that a:x=(a+b):(x:y)

Mathematics
1 answer:
frosja888 [35]3 years ago
6 0
We start by writing the ratio x:y and a:b as fraction

\frac{x}{x+y}: \frac{y}{x+y}  = \frac{a}{a+b}: \frac{b}{a+b}

This shows two pairs of equivalent fractions

\frac{x}{x+y}= \frac{a}{a+b} and \frac{y}{x+y}= \frac{b}{a+b}

We will use the first pair of fraction
\frac{x}{x+y}= \frac{a}{a+b} ⇒ cross multiply gives
x(a+b)=a(x+y) ⇒ then rearrange
\frac{a+b}{x+y} = \frac{a}{x} ⇒ which we can also write in form of ratio
(a+b):(x+y)=a:x

Hence it is proved that a:x=(a+b):(x+y) as required
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