# How do you simplify 3/5+(-6)?

Nov 7, 2016

$- \frac{27}{5}$

#### Explanation:

When you multiply two signs that are different the result is a minus (negative value)

Think of $+ \left(- 6\right) \text{ }$ as $\text{ } \left(+ 1\right) \times \left(- 6\right)$

Giving:$\text{ } - \left(1 \times 6\right) = - 6$

Putting it all together we have:

$\frac{3}{5} - 6$
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Multiply by 1 and you do not change the value. However, if you multiplied by $1 = \frac{5}{5}$ you would not change the value but you would change the way it looks.

$\textcolor{g r e e n}{\text{ "3/5-[6color(magenta)(xx1)]" "->" } \frac{3}{5} - \left[6 \textcolor{m a \ge n t a}{\times \frac{5}{5}}\right]}$

color(brown)("You can now do direct subtraction as denominators are the same"

$\text{ "3/5-30/5" "->" } \frac{3 - 30}{5}$

$\text{ " = " } - \frac{27}{5}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Foot note}}$

A fraction consist of " "("count")/("size indicator of what you are counting")

The difference in the function between the top number and the bottom number is very important.

" "("count")/("size indicator")" "->" "("numerator")/("denominator")

$\textcolor{w h i t e}{.}$

$\textcolor{g r e e n}{\overline{| \textcolor{w h i t e}{\frac{2}{2}} \text{You can not "color(red)(ul("directly"))" add or subtract the counts"color(white)(2/2)} |}}$ color(green)(ul(|color(white)(2/2)"unless the size indicators are the same."color(white)(" "2/2)|))

Consider this example:

You can directly add $3 + 2$ because their size indicators are the same. Really they are : $\frac{3}{1} + \frac{2}{1}$. It is just that people do not normally show them this way.