GRE Math : How to find order of operations

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Find Order Of Operations

Evaluate:

3 + 2(1 * 9 + 8) – 9/3

Possible Answers:

37/3

76/3

36

82

34

Correct answer:

34

Explanation:

Order of operations

Do everything inside the parenthesis first:

3 + 2(17) – 9/3

next, do multiplication/division

3 + 34 – 3

= 34

Example Question #2 : How To Find Order Of Operations

3 + 4 * 5 / 10 – 2 = 

Possible Answers:

5.5

5

1.5

3

7

Correct answer:

3

Explanation:

Here we must use order of operations. First we multiply 4 * 5 = 20. Then 20 / 10 = 2. Now we can do the addition and substraction. 3 + 2 – 2 = 3.  If you started at the beginning on the left hand side and not used order of operations, you would mistakenly choose 1.5 as the correct answer. 

Example Question #3 : How To Find Order Of Operations

Possible Answers:

Correct answer:

Explanation:

Order of operations can be remembered by PEMDAS (Please Excuse My Dear Aunt Sally): Parentheses Exponents Multiplication Division Addition Subtraction. 

[7(5 + 2) – (5 * 8)]2 = 

1: Inner parentheses   = [ 7(7) – 40 ]2

2: Outer brackets        = [ 49 – 40 ]2 = 92

3: Exponents               = 81

Example Question #4 : How To Find Order Of Operations

Possible Answers:

Correct answer:

Explanation:

This looks daunting as one long equation, but let's look at each piece and then add them all together. 

23 = 1/23 = 1/8

250 = 1

(–218)1 = –218

6251/4 = 5

(–27)1/3 = –3

Then, 23 + 250 + (–218)1 + 7/8 – 6251/4 + (–27)1/3 = 1/8 + 1 – 218 + 7/8 – 5 – 3 = –224.

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