Fractions must share a common denominator in order to be added or subtracted. The common denominator is the least common multiple of all the denominators.

The greatest common factor (GCF) is the greatest factor that divides two integers.

Arithmetic operations must be performed in the following specific order:

1. Parentheses
2. Exponents
3. Multiplication and Division (from L to R)
4. Addition and Subtraction (from L to R)

The acronym PEMDAS can help remind you of the order.

Percentages are ratios of an amount compared to 100. The percent change of an old to new value is equal to 100% x \({ new - old \over old }\).

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.