How do you simplify 5 7/8 + 3 5/12?

Mar 22, 2018

$9 \textcolor{w h i t e}{,} \frac{7}{24}$

Explanation:

Split it into 2 parts.

$\textcolor{g r e e n}{\textcolor{b l u e}{\text{Part 1: }} \to 5 + 3 = 8}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Part 2: }} \to \frac{7}{8} + \frac{5}{12}$

You can not DIRECTLY add or subtract fractions unless the bottom numbers (denominators) are the same.

Multiply by 1 and you do not change the value. However, 1 comes in many forms

$\textcolor{g r e e n}{\left[\frac{7}{8} \textcolor{red}{\times 1}\right] + \left[\frac{5}{12} \textcolor{red}{\times 1}\right] \textcolor{w h i t e}{\text{dddd")->color(white)("dddd}} \left[\frac{7}{8} \textcolor{red}{\times \frac{3}{3}}\right] + \left[\frac{5}{12} \textcolor{red}{\times \frac{2}{2}}\right]}$

color(green)(color(white)("ddddddddddddddddddddd")->color(white)("dddd")[color(white)("d") 21/24color(white)("d")]color(white)("d")+color(white)("d")[color(white)("d")10/24color(white)("d")] )

color(green)(color(white)("ddddddddddddddddddddd")->color(white)("dddd")31/24color(white)("dd")=color(white)("d")1 7/24
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting together Part1 and Part 2}}$

$\textcolor{w h i t e}{\text{dddddddddddddddd")8+1 7/24color(white)("d") = color(white)("d}} 9 \frac{7}{24}$