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.