# What is the difference and the product of (-5 3/5) and (-3 7/10)?

Jun 26, 2015

The difference, $\left(- 5 \frac{3}{5}\right) - \left(- 3 \frac{7}{10}\right) = \left(- 1 \frac{9}{10}\right)$

The product, $\left(- 5 \frac{3}{5}\right) \times \left(- 3 \frac{7}{10}\right) = \left(+ 20 \frac{18}{25}\right)$ is positive because when you multiply two negatives the result is positive.

#### Explanation:

Part 1: The difference
$\left(- 5 \frac{3}{5}\right) - \left(- 3 \frac{7}{10}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$= \left(- 5 \frac{3}{5}\right) + \left(3 \frac{7}{10}\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left(- 5 \frac{6}{10}\right) + \left(3 \frac{7}{10}\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{- 56 + 37}{10}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left(- \frac{19}{10}\right)$

Part 2: The product
(Note: combining a question about the difference with a question about the product was confusing. It should probably been asked as 2 questions).

$\left(- 5 \frac{3}{5}\right) \cdot \left(- 3 \frac{7}{10}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$= \left(- \frac{28}{5}\right) \cdot \left(- \frac{37}{10}\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= + \frac{1036}{50}$

$\textcolor{w h i t e}{\text{XXXX}}$$= 20 \frac{36}{50}$

A negative times a negative always gives a positive.