# Question #c86c2

Oct 6, 2017

$\frac{101}{26} \mathmr{and} 3 \frac{23}{26}$

#### Explanation:

Remember this rule of thumb: two minus signs gives a plus sign. That knocks out the first hurdle - those nasty double minus signs:

$2 \frac{5}{13} + 1 \frac{1}{2}$

Let's now rewrite both of these proper fractions as improper fractions:

$\frac{31}{13} + \frac{3}{2}$

Lastly, we need to set a common denominator. The best choice would be $26$, which you can find by multiplying the denominators together. Keep in mind, you can't magically replace the denominators with $26$, because that will just change the overall value of the fractions. Remember, we want to keep the same ratio. So for the first fraction, we can accomplish our goal by multiplying the numerator and denominator by $2$:

$\frac{62}{26}$

See? We have the denominator we want, and at the same time, the fraction is still equal to the original value of $\frac{31}{13}$. Let's now multiply the numerator and denominator of the second fraction by $13$:

$\frac{39}{26}$

Now that we have a common denominator for both fractions, we can add them:

$\frac{62 + 39}{26} = \frac{101}{26}$

Since the problem was given with proper fractions, you will most likely want your answer to be a proper fraction too.

$\frac{101}{26} = 3 \frac{23}{26}$