# How do you evaluate \frac { 1} { 4} + \frac { 3} { 2} + 5\frac { 1} { 3}?

Jun 22, 2017

$\frac{85}{12}$ or $7 \frac{1}{12}$

#### Explanation:

1. Convert $5 \frac{1}{3}$ into an improper fraction. Multiply 5 by 3, then add 1 to get the numerator. 3 remains the denominator.

$5 \frac{1}{3} = \frac{16}{3}$

2. We need to get a least common denominator (LCD) for all three fractions.

Multiples of 4: 4, 8, 12...
Multiples of 3: 3, 6, 9, 12...
Multiples of 2: 2, 4, 6, 8, 10, 12...

The smallest number that can be divided by 4, 2, and 3 is 12.

3. Multiply each fraction in the expression by a equivalent form of 1 so that each has a denominator of 12.

$\left(\frac{1}{4}\right) \left(\frac{3}{3}\right) + \left(\frac{3}{2}\right) \left(\frac{6}{6}\right) + \left(\frac{16}{3}\right) \left(\frac{4}{4}\right)$
$= \left(\frac{3}{12}\right) + \left(\frac{18}{12}\right) + \left(\frac{64}{12}\right)$

4. Add the fractions. Remember, when adding fractions, only add the numerators together and keep the denominators the same.

$= \frac{85}{12}$

Since $\left(\frac{85}{12}\right)$ is in simplest form, you could keep your answer as an improper fraction . You could also convert it into a mixed fraction, which would be $7 \frac{1}{12}$. (12 goes into 85 seven times, with a remainder of 1.)