# How do you simplify 7/8 + 5/6?

May 20, 2017

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#### Explanation:

A common method to solving this is to make the fractions have the same denominator for simpler addition.

This is done by multiplying as such:

$\textcolor{red}{\frac{6}{6}} \left(\frac{7}{\textcolor{b l u e}{8}}\right) + \left(\frac{5}{\textcolor{red}{6}}\right) \textcolor{b l u e}{\frac{8}{8}}$

Note that I have multiplied each fraction with a fraction that has the same numerator and denominator as the other fraction.

By multiplying $\frac{6}{6}$ and $\frac{8}{8}$, the fractions have not changed. Since $\frac{6}{6}$ and $\frac{8}{8}$ are equal to $1$ respectively.

$\textcolor{red}{\frac{6}{6}} \left(\frac{7}{\textcolor{b l u e}{8}}\right) + \left(\frac{5}{\textcolor{red}{6}}\right) \textcolor{b l u e}{\frac{8}{8}}$

$= \frac{42}{48} + \frac{40}{48}$

$= \frac{82}{48}$

Simplifying the fraction,

$= \left(\frac{82}{48}\right) \div \frac{2}{2}$

$= \frac{41}{24}$ or $1 \frac{17}{24}$