# How do you simplify [3/4 times 2/3 - (1/2 - 1/3)] 12 using PEMDAS?

Mar 15, 2016

4

#### Explanation:

$\left[\frac{3}{4} \times \frac{2}{3} - \left(\frac{1}{2} - \frac{1}{3}\right)\right] 12$

$\left[\frac{2}{4} - \left(\frac{3}{6} - \frac{2}{6}\right)\right] 12$

$\left[\frac{2}{4} - \left(\frac{1}{6}\right)\right] 12$

$\left[\frac{3}{6} - \frac{1}{6}\right] 12$

$\left[\frac{2}{6}\right] 12$

$\frac{24}{6}$

$4$

There's no "calculate this using PEMDAS". "PEMDAS" is obligatory, so "calculate this using PEMDAS" is a pleonasm.

Jun 6, 2018

$4$

#### Explanation:

$\left[\textcolor{b l u e}{\frac{3}{4} \times \frac{2}{3}} \text{ } \textcolor{g r e e n}{- \left(\frac{1}{2} - \frac{1}{3}\right)}\right] \times 12$

This is all one term, but within the brackets there are two terms.
Calculate them separately and simplify to a single number.

$= \left[\textcolor{b l u e}{\frac{\cancel{3}}{\cancel{4}} _ 2 \times \frac{\cancel{2}}{\cancel{3}}} \text{ } \textcolor{g r e e n}{- \left(\frac{3 - 2}{6}\right)}\right] \times 12$

$= \left[\textcolor{b l u e}{\frac{1}{2}} \text{ } \textcolor{g r e e n}{- \frac{1}{6}}\right] \times 12$

$= \left[\frac{3 - 1}{6}\right] 12$

$= \frac{2}{\cancel{6}} \times {\cancel{12}}^{2}$

$= 4$

Jun 6, 2018

$\left[\frac{3}{4} \times \frac{2}{3} - \left(\frac{1}{2} - \frac{1}{3}\right)\right] 12 = \textcolor{b l u e}{4}$

#### Explanation:

PEMDAS is an acronym that aids in remembering the order of operations:

Parenthesis/brackets
Exponents
Multiplication and Division in order from left to right.
Addition and Subtraction in order from left to right.

Simplify:

$\left[\frac{3}{4} \times \frac{2}{3} - \left(\frac{1}{2} - \frac{1}{3}\right)\right] 12$

Simplify $\left(\frac{1}{2} - \frac{1}{3}\right)$. Multiply each fraction by a fractional form of $1$ so that each fraction will have $6$ in the denominator. This will produce equivalent fractions that have the same value as the original fractions, but different numbers.

$\frac{1}{2} \times \frac{\textcolor{red}{3}}{\textcolor{red}{3}} - \frac{1}{3} \times \frac{\textcolor{b l u e}{2}}{\textcolor{b l u e}{2}} =$

$\frac{3}{6} - \frac{2}{6} =$

$\frac{1}{6}$

Place back into the expression

$\left[\frac{3}{4} \times \frac{2}{3} - \frac{1}{6}\right] 12$

Simplify $\frac{3}{4} \times \frac{2}{3}$ to $\frac{6}{12}$.

$\left[\frac{6}{12} - \frac{1}{6}\right] 12$

Simplify $\frac{6}{12}$ to $\frac{3}{6}$ by dividing the numerator and denominator by $2$.

$\left[\frac{3}{6} - \frac{1}{6}\right] 12$

Simplify $\frac{3}{6} - \frac{1}{6}$ to $\frac{2}{6}$.

$\left[\frac{2}{6}\right] 12$

Simplify $\frac{2}{6}$ to $\frac{1}{3}$.

$\left[\frac{1}{3}\right] \times 12$.

Simplify.

$\frac{12}{3}$

Simplify.

$4$