To multiply fractions: multiply numerators together and multiply denominators together. Simplify if possible.

Part = Whole × (Percent/100). Rearranging the percentage formula: Percent = Part/Whole × 100.

A number × its reciprocal = 1. Example: 3/4 × 4/3 = 1. This is the definition of a reciprocal.

a ≡ b (mod n) means a and b have the same remainder when divided by n. Example: 17 ≡ 2 (mod 5) since both give remainder 2.

Compound Interest A = P(1 + r/n)^(nt), where n = number of times compounded per year.

Area of equilateral triangle = (√3/4)s². All sides equal s; height = s√3/2.

To convert percent to decimal, divide by 100. Example: 75% = 75 ÷ 100 = 0.75.

Cross multiplication: if a/b = c/d, then a × d = b × c. Used to solve for an unknown in a proportion.

Diagonals = n(n-3)/2, where n is the number of sides. A square (n=4): 4(1)/2 = 2 diagonals.

Simple Interest I = P × r × t, where P = principal, r = rate, t = time.

Scientific notation: a × 10ⁿ where 1 ≤ a < 10. Example: 3,400 = 3.4 × 10³.

The complete list of prime factors with multiplicity is the prime factorization. Example: 12 = 2² × 3.

Speed = Distance / Time. Rearranged: Distance = Speed × Time; Time = Distance / Speed.

Percentage increase = (New - Old) / Old × 100. Always divide by the original (Old) value.

Percentage = (Part ÷ Whole) × 100. Divide the part by the whole, then multiply by 100.

Sum of interior angles in any triangle = 180°. This is a fundamental geometry fact used constantly.

In ratio a:b, total parts = a+b, so a represents a/(a+b) of the whole.

Sum of 1+2+3+...+n = n(n+1)/2. Example: 1+2+3+4+5 = 5×6/2 = 15.

Profit = Revenue - Cost (also called Selling Price - Cost Price). Positive profit = gain; negative = loss.

A perfect square is an integer × itself: 1, 4, 9, 16, 25, 36... Their square roots are whole numbers.