# Basics

An **integer** is a positive or negative number without a fractional or decimal component: -1, 2, 0.

An **even number** is an integer evenly divisible by two: -4, 0, 2, 8.

An **odd number** is an integer that is not evenly divisible by two: -5, 3, 9.

A **positive number** any number > 0. A **Negative number** any number < 0.

The sum of tree consecutive integers is three times the value of the middle number. \(3 + 4 + 5 = 4 * 3\).

“3 less than X” means “X - 3”.

- “If A, then B” -
**implication**. Let’s say that this is true. - “If B, then A” -
**converse**. May or may not be true. - “If not A, than not B” -
**inverse**. May or may not be true. - “If not B, then not A” -
**contrapositive**. Always true.

If fraction “\(5/10\)” \(5\) is **numerator** and \(10\) is **denominator**. Numerator increasing more rapidly than the denominator.

**Unit rate** is how much of something there is per one unit of something else (ex: 1 km/h).

Divisibility rules:

- \(1\) - all integers are divisible by 1.
- \(2\) - the last digit is even: 0, 2, 4, 6, 8.
- \(3\) - the sum of the digits is divisible by 3.
- \(4\) - the last two digits are divisible by 4.
- \(5\) - the last digit is 0 or 5.
- \(6\) - the number is divisible by 2 and 3.
- \(7\) - double the last digit. Subtract this value from the remaining digits. This number should be divisible by 7.
- \(8\) - the last three digits are divisible by 8.
- \(9\) - the sum of the digits is divisible by 9.