Question

Show that the proportions $\frac{a+b}{b}=\frac{c+d}{d}$ and $\frac{a}{b}=\frac{c}{d}$ are equivalent.

Short answer

The given proportion is equivalent.

Step-by-step solution

Step 1. Given information.

The given proportion is,

$\frac{a}{b}=\frac{c}{d}$.

Step 2. Formula used.

Two proportional are said to be equivalent, if one can be obtained from the other.

Step 3. Proof.

It is given, $\frac{a}{b}=\frac{c}{d}$

Two proportional are said to be equivalent if one can be obtained from the other.

Again, $\frac{a}{b}=\frac{c}{d}$

Adding 1 on both sides, doesn’t change the proportion.

$\begin{array}{l}\frac{a}{b}+1=\frac{c}{d}+1\\ \frac{a+b}{b}=\frac{c+d}{d}\end{array}$

Therefore, the given proportion is equivalent.