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

3 Answers
Mar 15, 2016

Answer:

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.

Jun 6, 2018

Answer:

#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#

Jun 6, 2018

Answer:

#[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#