# How do you express  7 3/5 + -4.8, as a simplified fraction?

May 13, 2016

$2 \frac{4}{5} \text{ another way of writing this is } \frac{14}{5}$

Every step in the calculation is shown.

#### Explanation:

$\textcolor{b r o w n}{\text{Assumption: 4.8 is a decimal value}}$

$\textcolor{b l u e}{\text{Consider } 4.8}$

This is the same $4 + \frac{8}{10}$

Multiply 4 by 1 but in the form of $1 = \frac{10}{10}$

$\left(4 \times \frac{10}{10}\right) + \frac{8}{10}$

$= \frac{40}{10} + \frac{8}{10} = \frac{48}{10}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Consider } 7 \frac{3}{5}}$

Multiply 7 by 1 in the form of $1 = \frac{5}{5}$

$\left(7 \times \frac{5}{5}\right) + \frac{3}{5}$

$\frac{35}{5} + \frac{3}{5} = \frac{38}{5}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting them together}}$

38/5-48/10" "color(red)("Correction "->+48/10" to "-48/10)

Multiply $\frac{38}{5}$ by 1 in the form of $1 = \frac{2}{2}$

$\left(\frac{38}{5} \times \frac{2}{2}\right) - \frac{48}{10}$

$\frac{76}{10} - \frac{48}{10} \text{ "=" } \frac{28}{10}$

$28 \div 10 \text{ "=" "2 +" remainder of } 8$

So $\frac{28}{10} = 2 \frac{4}{5}$