# Three-fourths of a number is 7/8. How do you find the number in lowest terms?

Feb 13, 2017

See the enter solution process below:

#### Explanation:

First, let's call the number we are looking for $n$/

In this problem the word "of" means to multiply or times.

"three fourths of a number is 7/8" can then be rewritten as:

$\frac{3}{4} \times n = \frac{7}{8}$

We can now solve for $n$ by multiplying each side of the equation by $\frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}}$ while keeping the equation balanced:

$\frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}} \times \frac{3}{4} \times n = \frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}} \times \frac{7}{8}$

$\frac{\cancel{\textcolor{red}{4}}}{\cancel{\textcolor{b l u e}{3}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} \times n = \frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}} \times \frac{7}{4 \times 2}$

$n = \frac{\cancel{\textcolor{red}{4}}}{\textcolor{b l u e}{3}} \times \frac{7}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 2}$

$n = \frac{7}{3 \times 2}$

$n = \frac{7}{6}$