# Question #92eb0

Jan 13, 2018

a. $\textcolor{b l u e}{n}$

#### Explanation:

$\frac{n}{4} + \frac{n}{4} + \frac{n}{4} + \frac{n}{4}$

$\textcolor{w h i t e}{\text{XXX}} = 4 \times \left(\frac{n}{4}\right)$

$\textcolor{w h i t e}{\text{XXX}} = n$

Jan 13, 2018

You can use Alan P.'s method or this method; they are both equally valid.

Remember that when you add fractions, you should find a common denominator. Luckily, these fractions all have the same denominator alreadyâ€”$4$.

The next step is simply to combine the fractions by keeping the denominator the same and taking all the numerators and adding them up in the numerator of the combined fraction.

$\frac{n}{4} + \frac{n}{4} + \frac{n}{4} + \frac{n}{4} = \frac{n + n + n + n}{4}$

Next, realize that $n + n + n + n = 4 n$ (you may want to remember that $n = 1 n$).

$\frac{n + n + n + n}{4} = \frac{4 n}{4}$

Now, since a fraction represents division, notice that the $4$ in the numerator can cancel with the $4$ in the denominator.

$\frac{4 n}{4} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} n}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} = n$