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Utilize PEMDAS to calculate a final value for the following expression:

(36-(2+4)2)3

Begin by evaluating every expression inside each set of PARENTHESES.

PEMDAS applies inside parentheses . . . The step-by-step procedure for evaluating expressions inside parentheses or square brackets is exactly the same as the step-by-step procedure for evaluating the overall expression . . .

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Sep 13, 2011
Evaluate Expression Using Order of Operations
by: Staff


The question:

[36-(2+4)2]3


The answer:


[36 - (2 + 4)2]3

[36 - (2 + 4)*2]*3


You can evaluate this expression using the PEMDAS order of operations. which tells you what to do first, second, . . . etc.


PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction



Step 1: you should evaluate the expression inside each set of PARENTHESES

PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

There are two nested parentheses. Begin with the inner parentheses:

(2 + 4)

(2 + 4) = (6)

After simplifying the expression inside the inner parentheses, your original expression looks like this:

[36 - (2 + 4)*2]*3

= [36 - (6)*2]*3

= [36 - 6*2]*3

Evaluate the expression inside the remaining PARENTHESES (square brackets in this case)

PEMDAS applies inside parentheses . . . The step-by-step procedure for evaluating expressions inside parentheses or square brackets is exactly the same as the step-by-step procedure for evaluating the overall expression . . .

[36 - 6*2]

What should do you do first? 36 - 6 or 6*2?

To answer this question, refer to the PEMDAS order:

When you follow PEMDAS, the first operation that should be completed is multiplication:

Parentheses (there are no parentheses inside the expression 36 - 6*2), exponents (there are no exponents in the expression 36 - 6*2), MULTIPLICATION (there is one multiplication inside the expression 36 - 6*2), division, addition, subtraction

6*2 = 12

After completing the multiplication indicated, your original expression inside the square brackets looks like this:

[36 - 12]

There is only one operation to complete:

36 - 12 = 24

After simplifying the expression inside the square brackets, your original expression looks like this:

[36 - (2 + 4)*2]*3

= [36 - (6)*2]*3

= [36 - 12]*3

= [24]*3

= 24*3



Step 2: evaluate EXPONENTS


PEMDAS order of evaluation for (simplified) overall expression: parentheses, EXPONENTS, multiplication, division, addition, subtraction

There are no exponents to evaluate.


Step 3: MULTIPLICATION


PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

There is one multiplication:

24*3 = 72



After completing the multiplication, you are finished.


The final answer to your question is: 72


A step-by-step recap of the entire process looks like this:

[36 - (2 + 4)*2]*3

= [36 - (6)*2]*3

= [36 - 12]*3

= [24]*3

= 24*3

= 72



Thanks for writing.

Staff
www.solving-math-problems.com



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