How do you evaluate #3- ( 1- ( - \frac { 11} { 2} ) )#?

2 Answers
Anthony R.
Sep 7, 2017

#-3.5#

Explanation:

Use "PEMDAS"

Parenthesis
Exponents
Multiplication/Division
Addition/Subtraction

We begin by working within the parenthesis

#3-(1-(-11/2))#

We see we have #(1-(-11/2))# We can rewrite this as

#1-(-11/2)->1--5.5->1+5.5#

And evaluate to get #6.5#

Our expression is now

#3-6.5#

Which equates to #-3.5#

Meave60
Sep 7, 2017

#3-(1-(-11/2))=color(teal)(-7/2#

Explanation:

A different approach, without writing fractions as decimals.

#3-(1-(-11/2))#

Simplify the parentheses.

#3-(1+11/2)#

Any whole number, #n#, has a denominator of #1#: #n=n/1#.

Rewrite.

#3/1-(1/1+11/2)#

The common denominator is #2#. Multiply the numerators and denominators of #3/1 and 1/1# by #color(magenta)2/color(magenta)2# to get equivalent fractions with #2# as the denominator.

#3/1xxcolor(magenta)2/color(magenta)2-(1/1xxcolor(magenta)2/color(magenta)2+11/2)#

Simplify.

#6/2-(2/2+11/2)#

Simplify the parentheses.

#6/2-(13/2)#

Subtract.

#-7/2#

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