# How do you add 6 3/4 + 5 1/8?

Nov 26, 2016

$\frac{95}{8}$ or $11 \frac{7}{8}$

#### Explanation:

First, we need to take these mixed fractions and convert them into improper fractions:

$6 \frac{3}{4} \implies \frac{\left(6 \cdot 4\right) + 3}{4} \implies \frac{24 + 3}{4} \implies \frac{27}{4}$

and

$5 \frac{1}{8} \implies \frac{\left(5 \cdot 8\right) + 1}{8} \implies \frac{40 + 1}{8} \implies \frac{41}{8}$

We can now restate the problem as:

$\frac{27}{4} + \frac{41}{8}$

We now need to get both fractions over a common denominator, in this case $8$, by multiplying the first fraction by the appropriate form of $1$:

$\left(\frac{2}{2} \cdot \frac{27}{4}\right) + \frac{41}{8} \implies \frac{54}{8} + \frac{41}{8} \implies \frac{95}{8}$

We can convert this to a mixed fraction if necessary by dividing 95 by 8 which is 11 with a remainder of 7 which can be written as $11 \frac{7}{8}$