


PreReview Review
Before diving into the math on the ACT tests, we very
quickly want to review the math the ACT assumes you know. The ACT
will not explicitly ask questions on these topics, but since the
test writers assume that you know them, many questions will indirectly
test them.
Order of Operations
You must know the order of operations for the test. The
best way to remember which operation gets performed before another
is the acronym PEMDAS, which stands for:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Exponents
Multiplication
Division
Addition
Subtraction
If you come across an equation that contains all of these
elements, you should first carry out the math within the parentheses,
then work out the exponents, then do the multiplication and the
division (working from left to right), and finally the addition
and subtraction, again working from left to right. For example,
take the expression:
You would first work out the math in the parentheses (following
PEMDAS even within the parentheses, meaning you should do multiplication
before subtraction):
Then work out the exponents:
Then do the multiplication:
Then the division:
Then the addition and subtraction:
Odd and Even Numbers
You should know about odd and even numbers and the differences
between them. For this topic, however, we will provide a very quick
review.
Even Numbers
Even numbers are numbers that are divisible by 2 with
no remainder. Remember that 0 is included in this definition.
Odd Numbers
Odd numbers are numbers that, if divided by 2,
will leave a remainder of 1.
Operations and Odd and Even Numbers
There are a number of rules regarding operations and odd
and even numbers that you should know instinctively.
Addition  Subtraction  Multiplication  
+  Odd  Even  –  Odd  Even  x  Odd  Even  
Odd  Even  Odd  Odd  Even  Odd  Odd  Odd  Even  
Even  Odd  Even  Even  Odd  Even  Even  Even  Even 
Signed Numbers
The term “signed numbers” refers to numbers that include
either a positive or negative sign, and are therefore marked as
being either greater than zero (positive) or less than zero (negative).
Zero has no sign.
Students who are comfortable with positive numbers sometimes
get confused when dealing with negative numbers. For example, while
positive numbers become larger as they move farther away from zero,
negative numbers become smaller: –10 is a smaller number
than –1. When dealing with negative numbers, be careful
not just to see the 10 in –10 and assume
that it is a larger number than –1, unless you are
dealing with absolute value, which is covered later in this chapter.
Negative Numbers and Operations
Negative numbers behave differently than positive numbers
when you perform various operations on them. In terms of addition
and subtraction, negative numbers invert the operations.
Adding Signed Numbers
When a negative number is added to another number, the
sum will be a smaller number. In fact, adding a negative number
is the same as subtracting a positive number of the same absolute
value (see p. ).
Subtracting Signed Numbers
When a negative number is subtracted from another number,
the difference will be a larger number. In fact, subtracting a negative
number is the same as adding a positive number of the same value.
Multiplying and Dividing with Negative Numbers
Negative numbers also follow sign rules when you multiply
or divide them:
Positive  Negative  
Positive  Positive  Negative 
Negative  Negative  Positive 
