# Show that in the Denominator Addition/Subtraction Property of proportions: If a/ b = c/ d, then ( a + b)/ b = ( c + d)/ d or ( a − b)/ b = ( c − d)/ d?

## Show that in the Denominator Addition/Subtraction Property of proportions: If $\frac{a}{b} = \frac{c}{d}$, then $\frac{a + b}{b} = \frac{c + d}{d}$ or ( a − b)/ b = ( c − d)/ d?

##### 1 Answer
Apr 22, 2016

Please see below.

#### Explanation:

As $\frac{a}{b} = \frac{c}{d}$ ............(1)

adding $1$ to both sides

$\frac{a}{b} + 1 = \frac{c}{d} + 1$ or $\frac{a}{b} + \frac{b}{b} = \frac{c}{d} + \frac{d}{d}$ or

$\frac{a + b}{b} = \frac{c + d}{d}$ ............(2)

Now subtracting $1$ from both sides

$\frac{a}{b} - 1 = \frac{c}{d} - 1$ or $\frac{a}{b} - \frac{b}{b} = \frac{c}{d} - \frac{d}{d}$ or

$\frac{a - b}{b} = \frac{c - d}{d}$ ............(3)

In fact dividing (2) by (3) also gives us

$\frac{a + b}{a - b} = \frac{c + d}{c - d}$ ............(2)