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Arithmetic Laws — Quick Reference
Commutative
a + b = b + a · a × b = b × a
a
b
b
a
Associative
(a + b) + c = a + (b + c)
Group left →
a
b
c
Group right → a + (b + c)
Distributive
a × (b + c) = a×b + a×c
a×b
a×c
a
b
c
Identity · Zero · Inverse
Identity: a + 0 = a · a × 1 = a
Zero: a × 0 = 0
Additive inverse: a + (−a) = 0
Multiplicative inverse: a × (1/a) = 1 (a≠0)
Order of Operations
PEMDAS / BODMAS
Parentheses
Exponents
× / ÷
+ / −
Example:
3 + 2 × (4 + 1) = 3 + 2 × 5 = 3 + 10 =
13
MeBest Cheatsheet — Arithmetic Laws (SVG)