A Guide to the GRE/Order of Operations

Order of Operations

The order of mathematical operations is parentheses, exponents, multiplication and division, and finally, addition and subtraction.

The acronym is “Please Excuse My Dear Aunt Sally.”

Within these categories, it doesn't matter which operation is performed first. Init doesn't matter whether 6 is divided by the 7 first or multiplied by the 8 first; the result will be the same. However, with parentheses, the interior parentheses must be worked out prior to working out any exterior parentheses. 2(3(4 + 5)) requires adding the 4 and 5 before multiplying the result by 3.

“Divide bars” operate as parentheses.

Inthe 6 and 7 are added first, unlike inor a similar expression.

Practice

1. What is the value of?

2. If= 45 then what does q equal?

3. If 5(6²)(3 + 2) = 5 + e, what is the value of e?

Answers to Practice Questions

1. 6

Subtract the 2 from the 3 first, then multiply the 5 by the 1, then add the 4 to the 5. Multiply the 6 by the 9, then divide by 9 to arrive at 6.

2. 13

Start with the initial equation.

Work out the parentheses.

Multiply both sides by 7.

Expand the parentheses.

Subtract 24 from both sides.

Divide both sides by 3. q is 13.

3. 895

5(6²)(3 + 2) = 5 + e Start with the initial equation.

5(36)(5) = 5 + e Work out the operations inside the parentheses.

900 = 5 + e Multiply the parenthetical amounts together.

895 = e Subtract 5 from both sides. e is 895.