Numbers and operations is the area in ACT Math used in most of the word problems and problems involving percentages, averages, and sequences.
Number Classifications
All numbers can be put into one or more of the following classes. In the ACT Math you will only deal in whole numbers and fractions. While all fractions can be represented in decimal form, it is generally advisable to keep them as fractions. All multiple choice selections will be presented in either fraction or whole number form.
Integers: are whole numbers. All integers greater than zero are known as positive integers, and all integers less than zero are known as negative integers. Zero is neither positive nor negative.
Consecutive Integers: are integers in sequence, without skipping any integers. An example of this is the series {9,10,11,12,13,14}. A consecutive integer series may also include zero, for example the series {-2,-1,0,1,2,3).
Odd Integers: are all of the integers that have a remainder 1 when divided by 2. So, {1,3,5,7,9,11,13,…}. The negatives of any of these numbers is also odd, so another example of a set of odd numbers is {…,-3,-1,1,3,5,…}.
Even Integers: are all integers that are divisible by 2 with no remainder. Zero is considered an even number, despite the fact that it is neither positive nor negative and not divisible by 2.
Some Rules Regarding even and odd numbers:
even ± even = even
even ± odd = odd
odd ± odd = even
even × even = even
even × odd = even
odd × odd = odd
Prime Numbers: are numbers that are divisible with no remainder by only 1 and itself. By definition 1 is not considered a prime number, the smallest prime number is 2. The set of prime numbers includes {2,3,5,7,11,13,17,…} It is important to know how to factorize non prime numbers into prime numbers, so if you’re uncertain, you should read our post on it.
Want to try out an ACT math question on your own? Here’s one from Grockit!
