Addition and Subtraction
2-1Basic Assumptions
Overview
Algebra rests on number properties: closure, commutativity, associativity, identity, and inverse.
Key ideas
- Commutative: a + b = b + a; ab = ba.
- Associative: (a + b) + c = a + (b + c).
- Identity: a + 0 = a; a · 1 = a.
Worked examples
Example 1
Problem. Which property: 5 + 7 = 7 + 5?
Solution. Commutative property of addition.
Example 2
Problem. Which property: 3·(4·2) = (3·4)·2?
Solution. Associative property of multiplication.
Practice
Try each one. Click Show answer when ready.
- 1.
Name the property: x + 0 = x.
- 2.
Name the property: 6·1 = 6.
- 3.
Name the property: 2(3 + x) = 2·3 + 2·x.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Use the basic assumptions to simplify 4·(5·x) + 3·(2·y).
- 2.
Use the basic assumptions to simplify (3 + a) + 7.