division, and no priority between addition and subtraction. When choosing
between these operations, always move from left to right. The following list outlines
what each operation represents:■ Parentheses ( ) or [ ]: parentheses are used to bracket off part of an
expression from the rest of the expression. For example: (3 + 5) × 2.
■ Exponents 43 , 3^5 , and so on: exponents tell you how many times you
multiply the base by itself. 4^3 is the same as 4 × 4 × 4. 3^5 is the same
as 3 × 3 × 3 × 3 × 3.
■ Roots √ 16, √ 8 , and so on: roots are the opposite of exponents. In terms of
PEMDAS, roots take the same priority as exponents. To get the square root of
a number, you need to determine which value, when multiplied by itself, will
yield the number under the square root.
For example, √ 16 = 4, since 4 × 4 = 16.
■ Multiplication 3 × 4; (3)(4); xy: Note that multiplication is the opposite of
division. If you multiply 3 times 4 and then divide that result by 4, the result
is 3.
■ Division,^62 : Next, you will evaluate any expressions that require multiplication
or division. Note: There is no hierarchy between multiplication and division!
When presented with these two operations, always work from left to right:
6 divided by 3 × 9 → First do 6 ÷ 3 = 2, then 2 × 9 = 18.
■ Addition/Subtraction 4 + 7 + 11; 8 – 3 = 5: Next, you will evaluate
any expressions that require addition or subtraction. Note: Just as with
multiplication and division, there is no priority between addition and
subtraction! When presented with these two operations, always work from
left to right:
7 − 9 + 5 → First, do 7 – 9 = −2, then do −2 + 5 = 3.Now that you’ve reviewed PEMDAS, let’s work through the question at the
beginning of this section:
(8 + 1)^2 divided by 3 × (5 + 2)
You see two expressions within parentheses, so first evaluate those
expressions:
92 divided by 3 × 7
Next, you see a term raised to an exponent, so evaluate that term:
81 divided by 3 × 7
Now you are left with division and multiplication. Remember, there’s no
priority between these two operations. Just work from left to right.
81 divided by 3 = 27
↓
27 × 7 = 1893258 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 258 12/05/17 11:53 am