# How do you solve and check your solution given 3 3/4+n=6 5/8?

Apr 11, 2017

$n = \frac{23}{8} = 2 \frac{7}{8}$

#### Explanation:

First it would be useful to turn your fractions into improper fractions. This is so you can add and subtract them easily.

$\text{ } 3 \frac{3}{4} + n = 6 \frac{5}{8}$

$\left[1\right] \text{ } \frac{15}{4} + n = \frac{53}{8}$

Now your goal is to only have $n$ on one side. We will do this by subtracting $\frac{15}{4}$ from both sides.

$\left[2\right] \text{ } \frac{15}{4} + n - \frac{15}{4} = \frac{53}{8} - \frac{15}{4}$

You may cancel $\frac{15}{4}$ on the right side now, since $\frac{15}{4} - \frac{15}{4} = 0$.

$\left[3\right] \text{ } n = \frac{53}{8} - \frac{15}{4}$

You can simplify this further by combining $\frac{53}{8}$ and $\frac{15}{4}$. But you will first need to make sure they have the same denominator. So multiply $\frac{15}{4}$ by $\frac{2}{2}$. This is valid because $\frac{2}{2} = 1$. Once you do this, both fractions will now have the same denominator.

$\left[4\right] \text{ } n = \frac{53}{8} - \left(\frac{15}{4}\right) \left(\frac{2}{2}\right)$

$\left[5\right] \text{ } n = \frac{53}{8} - \frac{30}{8}$

$\left[6\right] \text{ } n = \frac{53 - 30}{8}$

$\left[7\right] \text{ } \textcolor{b l u e}{n = \frac{23}{8} = 2 \frac{7}{8}}$