Math Formulas
A collection of commonly used math formulas and arithmetic rules for elementary school students.
➕ Addition & Subtraction
Commutative Property of Addition
a + b = b + a
Example: 3 + 5 = 5 + 3 = 8
Associative Property of Addition
(a + b) + c = a + (b + c)
Example: (2 + 3) + 4 = 2 + (3 + 4) = 9
Identity Property of Addition
a + 0 = a
Example: 7 + 0 = 7
Definition of Subtraction
a - b = c → b + c = a
Example: 8 - 3 = 5 → 3 + 5 = 8
Identity Property of Subtraction
a - 0 = a
Example: 9 - 0 = 9
Self-Subtraction
a - a = 0
Example: 6 - 6 = 0
✖️ Multiplication & Division
Commutative Property of Multiplication
a × b = b × a
Example: 3 × 4 = 4 × 3 = 12
Associative Property of Multiplication
(a × b) × c = a × (b × c)
Example: (2 × 3) × 4 = 2 × (3 × 4) = 24
Distributive Property
a × (b + c) = a × b + a × c
Example: 3 × (4 + 5) = 3 × 4 + 3 × 5 = 27
Identity Property of Multiplication
a × 1 = a
Example: 8 × 1 = 8
Multiplication by Zero
a × 0 = 0
Example: 7 × 0 = 0
Definition of Division
a ÷ b = c → b × c = a
Example: 12 ÷ 3 = 4 → 3 × 4 = 12
⚖️ Comparison
Reflexive Property
a = a
Example: 5 = 5
Symmetric Property
a = b → b = a
Example: 3 + 4 = 7 → 7 = 3 + 4
Transitive Property
a > b, b > c → a > c
Example: 5 > 3, 3 > 1 → 5 > 1
Addition Property of Inequality
a > b → a + c > b + c
Example: 5 > 3 → 5 + 2 > 3 + 2