Question

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

Answer 1

4

Explanation:

`[3/4xx2/3-(1/2-1/3)]12`

`[2/4-(3/6-2/6)]12`

`[2/4-(1/6)]12`

`[3/6-1/6]12`

`[2/6]12`

`24/6`

`4`

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

Answer 2

`4`

Explanation:

`[color(blue)(3/4 times 2/3)" "color(green)( - (1/2 - 1/3))]xx 12`

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

`=[color(blue)(cancel3/cancel4_2 times cancel2/cancel3)" "color(green)( - ((3-2)/6))]xx 12`

`=[color(blue)(1/2)" "color(green)( - 1/6)]xx 12`

`=[(3-1)/6] 12`

`=2/cancel6 xx cancel12^2`

`=4`

Answer 3

`[3/4xx2/3-(1/2-1/3)]12=color(blue)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:

`[3/4xx2/3-(1/2-1/3)]12`

Simplify `(1/2-1/3)`. 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.

`1/2xxcolor(red)3/color(red)3-1/3xxcolor(blue)2/color(blue)2=`

`3/6-2/6=`

`1/6`

Place back into the expression

`[3/4xx2/3-1/6]12`

Simplify `3/4xx2/3` to `6/12`.

`[6/12-1/6]12`

Simplify `6/12` to `3/6` by dividing the numerator and denominator by `2`.

`[3/6-1/6]12`

Simplify `3/6-1/6` to `2/6`.

`[2/6]12`

Simplify `2/6` to `1/3`.

`[1/3]xx12`.

Simplify.

`12/3`

Simplify.

`4`