Simplify:

#7 1/2-(1/9+2/3)-:3/2#

Follow the order of operations as indicated by the acronym PEMDAS:

Parentheses/brackets

Exponents/radicals

Multiplication and Division in order from left to right.

Addition and Subtraction in order from left to right.

Simplify the parentheses.

#(1/9+2/3)#

In order to add or subtract fractions, they must have the same denominator, called the least common denominator (LCD).

The LCD is #9#. Multiply #2/3# by #3/3# to get an equivalent fraction with a denominator of #9#. Since #3/3=1#, the numbers will change, but the value remains the same.

#1/9+2/3xx3/3=#

#1/9+6/9=#

#7/9#

Rewrite the expression.

#7 1/2-7/9-:3/2#

Carry out the division next. Since we are dividing by a fraction, we invert it and multiply.

#7 1/2-7/9xx2/3#

#7 1/2-(7xx2)/(9xx3)#

#7 1/2-14/27#

Convert #7 1/2# to an improper fraction by multiplying the denominator by the whole number and adding the numerator. Place the result over the denominator of #2#.

#((2xx7+1))/2-14/27#

Simplify.

#15/2-14/27#

The denominators #2# and #27# do not have a common multiple, so to get the LCD, we multiply the denominators.

LCD#=##2xx27=54#

Multiply #15/2# by #27/27#, and multiply #14/27# by #2/2# to get equivalent fractions with #54# as the denominator.

#15/2xx27/27-14/27xx2/2#

#(15xx27)/(2xx27)-(14xx2)/(27xx2)#

Simplify.

#405/54-28/54=377/54#