Question

If $\frac{a}{b}=\frac{c}{d}$ ($a,b,c,d$ positive numbers), which one of the following is not always true?

• A. $\frac{a}{c}=\frac{b}{d}$
• B. $\frac{b}{a}=\frac{d}{c}$
• C. $\frac{a+b}{b}=\frac{c+d}{d}$
• D. $\frac{a}{d}=\frac{b}{c}$
• E. $\frac{a}{b}=\frac{a+c}{b+d}$

Answer 1

The correct option is D $\frac{a}{d}=\frac{b}{c}$

Given, $\frac{a}{b}=\frac{c}{d}$
which is equivalent to $\frac{a}{c}=\frac{b}{d}$, $\frac{b}{a}=\frac{d}{c}$ , $\frac{a+b}{b}=\frac{c+d}{d}$, $\frac{a}{b}=\frac{a+c}{b+d}$
But $\frac{a}{d}\ne \frac{b}{c}$
So, the correct answer is option $D$.