# How do you add -9/8+7/4?

Sep 20, 2016

$- \frac{9}{8} + \frac{7}{4} = \frac{5}{8}$

#### Explanation:

WE have denominators $4$ and $8$ here and their GCD is $8$, hence we can add them by converting them to common GCD.

$- \frac{9}{8} + \frac{7}{4}$

= $- \frac{9}{8} + \frac{7 \times 2}{4 \times 2}$

= $- \frac{9}{8} + \frac{14}{8}$

= $\frac{- 9 + 14}{8}$

= $\frac{5}{8}$

Sep 21, 2016

$\frac{5}{8}$

#### Explanation:

Fraction$\to \left(\text{count")/("size indicator")->("numerator")/("denominator}\right)$
$\textcolor{w h i t e}{.}$

Size indicator is how many of what you are counting to make a whole 1 of something.

$\textcolor{w h i t e}{.}$
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Point 1}}$

We need to add/subtract counts but we can only do this 'directly' if the 'size indicators' (denominators) are the same.

$\textcolor{b l u e}{\text{Point 2}}$
Multiply by 1 and you do not change the intrinsic value. However, 1 comes in many forms. So we can change the way something looks but not change its intrinsic value.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:$\text{ } - \frac{9}{8} + \frac{7}{4}$

Change the order:

$\frac{7}{4} - \frac{9}{8}$

This is the same in value as:

$\left(\frac{7}{4} \textcolor{m a \ge n t a}{\times 1}\right) - \frac{9}{8}$

But write 1 as $1 = \frac{2}{2}$ giving:

$\left(\frac{7}{4} \textcolor{m a \ge n t a}{\times \frac{2}{2}}\right) - \frac{9}{8} \text{ "->" } \frac{7 \times 2}{4 \times 2} - \frac{9}{8}$

$\frac{14}{8} - \frac{9}{8} = \frac{5}{8}$