Proportions: given a/b = c/d, prove a+b/b = c+d/d

[sagar1127]

How and what would be the answer to this question:

If a/b = c/d

Show your work on how you can get that to this:
a+b/b = c+d/d

 

[pka]

Add 1 to both sides.
Realize that: \(\displaystyle \frac {b} {b} = \frac {d} {d} = 1\)

 

[sagar1127]

Thx but what you are saying is that to make that into the second part all you have to do is add 1 to each side.

 

[pka]

\(\displaystyle \L \begin{array}{rcl}
\frac{a}{b} & = & \frac{c}{d} \\
\frac{a}{b} + 1 & = & \frac{c}{d} + 1 \\
\frac{a}{b} + \frac{b}{b} & = & \frac{c}{d} + \frac{d}{d} \\
\frac{{a + b}}{b} & = & \frac{{c + d}}{d} \\
\end{array}\)