# What is (-2/3)/(1/4) + 1/2 xx 1/2 xx 1/3?

## It confuses me, too many fractions.

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1
Feb 6, 2018

$= - 2 \frac{7}{12}$

#### Explanation:

There is no need to get confused....... count the number of terms and then simplify each term separately.

In the last step you can add the answers to the terms together,

Terms are separated by $+ \mathmr{and} -$ signs, so there are $2$ terms:

$\textcolor{b l u e}{\frac{- \frac{2}{3}}{\frac{1}{4}}} \text{ "+" } \textcolor{red}{\frac{1}{2} \times \frac{1}{2} \times \frac{1}{3}}$

=color(blue)(-2/3 div1/4)" "+" "color(red)(1/12" "(larr "top x top x top")/(larr"bottom x bottom x bottom")
$\textcolor{w h i t e}{\times . \times x} \downarrow$
$= \textcolor{b l u e}{- \frac{2}{3} \times \frac{4}{1}} \text{ "+" } \textcolor{red}{\frac{1}{12}}$

$= \textcolor{b l u e}{- \frac{8}{3}} \text{ "+" "color(red)(1/12)" } \leftarrow$ find a common denominator
$\text{ } \downarrow$
$\textcolor{b l u e}{- \frac{8}{3} \times \frac{4}{4}}$
$\text{ } \downarrow$
=color(blue)(-32/12" "+" "color(red)(1/12)" "larr now add the numerators

$= \frac{- 32 + 1}{12}$

$= - \frac{31}{12}$

$= - 2 \frac{7}{12}$

Then teach the underlying concepts
Don't copy without citing sources
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Write a one sentence answer...

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Explain in detail...

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1
Feb 3, 2018

$- \frac{31}{12}$

#### Explanation:

$\frac{- \frac{2}{3}}{\frac{1}{4}} + \frac{1}{2} \times \frac{1}{2} \times \frac{1}{3}$

Divide $- \frac{2}{3}$ by $\frac{1}{4}$

$\frac{- \frac{2}{3}}{\frac{1}{4}} = - \frac{2}{3} \times \frac{4}{1} = - \frac{8}{3}$

So

$- \frac{8}{3} + \frac{1}{2} \times \frac{1}{2} \times \frac{1}{3}$

Multiply $\frac{1}{2}$ by $\frac{1}{2}$

$- \frac{8}{3} + \frac{1}{4} \times \frac{1}{3}$

Multiply $\frac{1}{4}$ by $\frac{1}{3}$

$- \frac{8}{3} + \frac{1}{12}$

Use the common denominator

$- \frac{32}{12} + \frac{1}{12}$

Add $- \frac{32}{12}$ and $\frac{1}{12}$

$- \frac{31}{12}$

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