Number Rules
Consecutive Numbers
Divisibility
Fractions
Decimals
Exponents
Roots & Radicals
Note: this section is designed as an introduction for students scoring in the middle to low ranges.
Number Definitions
Integer
a member of the set of positive whole numbers {1, 2, 3, . . . }, negative whole numbers {-1, -2, -3, . . . }, and zero. Fractions and decimals are not integers. Integers are also called "whole numbers".
Positive number
a number greater than zero, such as +5 (usually written simply as 5).
Negative number
a number less than zero, such as -5.
Zero
is neither positive nor negative and is an integer.
Rational number
a number that may be expressed as integers, decimals or fractions (a ratio of integers), as opposed to an...
Irrational number
a number that cannot be expressed by the ratio of two integers, such as π or √2. Very mysterious! Note: anything divided by zero is irrational.
If you forget a rule (this happens all the time under test day pressure) consider using Experiments or Backsolving/Plug-In to get around it (we discuss these advanced strategies in II. General Math Strategies).
ORDER OF OPERATIONS - PEMDA
Take a look at:
5 + 2 × 3, what is it?
(5 + 2) × 3 = (7) × 3 = 21
Add first, then multiply
or?
5 + (2 × 3 ) = 5 + (6) = 11
Multiply first, then add
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