Integrated Math 1 / Unit 1: Quantities and Expressions
1.4 Properties of Operations
Notes
Properties let you rewrite expressions in equivalent forms and justify each step.
- Commutative: order does not matter for addition or multiplication: $a + b = b + a$.
- Associative: grouping does not matter: $(a + b) + c = a + (b + c)$.
- Distributive: $a(b + c) = ab + ac$.
- Identity: $a + 0 = a$ and $a \cdot 1 = a$. Inverse: $a + (-a) = 0$ and $\displaystyle a \cdot \frac{1}{a} = 1$.
- Example: $6 \cdot 47 = 6(50 - 3) = 300 - 18 = 282$.
Practice
Which property does $5(x + 3) = 5x + 15$ show?
The 5 multiplies each term inside the parentheses.
Which equation shows the commutative property of addition?
Commutative means the order of the numbers is swapped.
Using the distributive property, $6 \cdot 47 = 6(50 - 3)$. What is the value?
$300 - 18 = 282$.
Ready for more? Take the Unit 1 test.