Properties of Real Numbers Algebra 2014/2015

I can use the properties of real numbers correctly. AIM I can use the properties of real numbers correctly. TOPIC: Properties of Numbers

DO NOW How can we represent the distributive property as an algebraic formula?

Distributive Property If a, b, and c are real numbers, then a(b+c)= ab + ac Example: 7(m+4)

Distributive Property Example: 6 – 2 (k + 3) Example: (m - 4)(m + 2)

Commutative Property of Addition Does 3 + 4 = 4 + 3?

Commutative Property of Multiplication Does 3 * 4 = 4 * 3? Can we represent this geometrically? Does 2 * 3 * 4 = 4 * 2 * 3?

Associative Property of Addition Does 3 + (4 + 5) = (3 + 4) + 5?

Associative Property of Multiplication Does 3 * (4 * 5) = (3 * 4) * 5?

If a, b, and c are real numbers… Commutative Property of Addition: a + b = b + a. Commutative Property of Multiplication: a × b = b × a. Associative Property of Addition: (a+b)+c = a + (b+c) Associative Property of Multiplication: (ab)c =a(bc).

Commutative Property Continued Does it work with three numbers? Can we re-arrange all three numbers?

Property of Equality If two sides of an equation are balanced, we can preserve the balance by adding or multiplying number to both sides. Example: Addition Multiplication k = 4 b = 6 k + 3 = 4 + 3 b • 4 = 6 • 4

Identity Property How can we multiply or add to disguise the variable S, but not change its identity. S = S + S = S •

Inverse Properties Think of a synonym for inverse: What would happen if we added or multiplied by the inverse of a variable? J + (-J) = .

Homework: Properties WS EXIT TICKET Pick any property you learned in class today and describe it in your own words. Homework: Properties WS