GMAT Exam: A Simple Guide To Arithmetic - Order of Operations

Grouping Symbols
Grouping symbols such as parentheses ( ), brackets [ ], and curly braces { } are used to keep things together that belong together.

Fraction bars, absolute value bars, and radicals also are grouping symbols.

When you are performing computations, perform operations in grouping symbols first. It is very important that you do so when you have addition or subtraction inside the grouping symbol.

For instance, (5 – 3)3 ≠ 53 – 33; (5 – 3)3 = 23 = 8, but 53 – 33 = 125 – 27 = 98.

When you no longer need the grouping symbol, omit it.

PEMDAS
Follow the order of operations when you evaluate numerical expressions:
1.Do computations inside Parentheses (or other grouping symbols). If there is more than one operation inside the grouping symbol, follow the order of operations given here to do the computations inside the parentheses. If there are grouping symbols within grouping symbols, start with the innermost grouping symbols.
2.Evaluate Exponential expressions (also, evaluate absolute value, square root, and other root expressions).
3.Multiply and Divide in the order in which they occur from left to right.
4.Add and Subtract in the order in which they occur from left to right.

Try the mnemonic “Please Excuse My Dear Aunt Sally”—abbreviated as PEMDAS—to help you remember the order of operations.

The first letters stand for “Parentheses, Exponentiation, Multiplication, Division, Addition, and Subtraction.”

Example:

Evaluate .

First, compute inside grouping symbols.

Next, evaluate exponents and roots.

Then, multiply and divide from left to right.
= 90 – 45 + 7

Finally, add and subtract from left to right.
= 52