# An attorney drove 7 1/4 miles from his home to a client's home and another 5 2/5 miles to get to his office. How far did he drive in total?

Oct 22, 2016

The attorney drove $\frac{253}{20}$ miles, which is $12 \frac{13}{20}$ miles as a mixed fraction.

#### Explanation:

Add $7 \frac{1}{4} \textcolor{w h i t e}{1} \text{mi}$ and $5 \frac{2}{5} \textcolor{w h i t e}{1} \text{mi}$.

First convert each fraction to an improper fraction by multiplying the denominator by the whole number and then adding the numerator. Place the result over the original denominator.

$7 \frac{1}{4} = \frac{4 \times 7 + 1}{4} = \frac{29}{4}$

$5 \frac{2}{5} = \frac{5 \times 5 + 2}{5} = \frac{27}{5}$

The problem now looks like this:

$\frac{29}{4} + \frac{27}{5}$

Only fractions with the same denominator can be added or subtracted. The least common denominator (LCD) must be determined. One way to do this is by writing the multiples for each denominator. The first one that is the same for both denominators is the LCD.

$4 :$ $4 , 8 , 12 , 16 , \textcolor{red}{20} , 24 , 25$

$5 :$ $5 , 10 , 15 , \textcolor{red}{20}$

The LCD is $20$.

Now multiply each fraction by an $\textcolor{red}{\text{equivalent fraction}}$ that will convert the denominator of each to the LCD.

$\frac{29}{4} \times \textcolor{red}{\frac{5}{5}} + \frac{27}{5} \times \textcolor{red}{\frac{4}{4}}$

Simplify.

$\frac{145}{20} + \frac{108}{20} = \frac{253}{20}$ miles

You can leave the answer as an improper fraction or you can convert it to a mixed fraction. To do this, use long division to divide the numerator by the denominator. The whole number part is the whole number of the mixed fraction, the remainder is the numerator.

$253 \div 20 = 12 \textcolor{w h i t e}{1} \text{with a remainder of 13}$

The mixed fraction is $12 \frac{13}{20}$ miles.