# How do you simplify  (8/125) -1/3?

Mar 17, 2016

$\frac{8}{125} - \frac{1}{3} = \textcolor{b l u e}{- \frac{101}{375}}$

#### Explanation:

In order to add or subtract fractions, they must have the same denominator, which is called the least common denominator (LCD).

$\frac{8}{125} - \frac{1}{3}$

Find the LCD by prime factorization of both denominators.

$125 = 5 \times 5 \times 5$
$3 = 3$

Multiply the prime factors to get the LCD.

$\text{LCD} = 3 \times 5 \times 5 \times 5 = 375$

Multiply each fraction by a factor that will give each fraction the denominator $375$.

$\left(\frac{8}{125} \times \frac{3}{3}\right) - \left(\frac{1}{3} \times \frac{125}{125}\right)$

Simplify.

$\frac{24}{375} - \frac{125}{375} =$

$\frac{- 101}{375} =$

$- \frac{101}{375}$