# Bill ate 1/4 pound of trail mix on his first break during a hiking trip. On his second break, he ate 1/6 pound. How many pounds of trail mix did he eat during both breaks?

Aug 8, 2017

See a solution process below:

#### Explanation:

We can write that on his two breaks Bill at:

$\left(\frac{1}{4} + \frac{1}{6}\right) \text{lb}$ of trail mix.

We now need to put the two fractions over a common denominator in order to add the fractions. The LCD for these two fractions is $12$. We need to multiply each fraction by the appropriate form of $1$ to ensure each fraction has a denominator of $12$:

$\left(\left[\frac{3}{3} \times \frac{1}{4}\right] + \left[\frac{2}{2} \times \frac{1}{6}\right]\right) \text{lb} \implies$

$\left(\left[\frac{3 \times 1}{3 \times 4}\right] + \left[\frac{2 \times 1}{2 \times 6}\right]\right) \text{lb} \implies$

$\left(\frac{3}{12} + \frac{2}{12}\right) \text{lb} \implies$

$\frac{3 + 2}{12} \text{lb} \implies$

$\frac{5}{12} \text{lb}$

Bill ate $\frac{5}{15} \text{lb}$ of trail mix on the two breaks.