Properties of Real Numbers Commutative Property of Addition

Properties of Real Numbers • Commutative Property of Addition a+b=b+a Ex) (- 7) + ( 3) = ( 3) + ( -7) = - 4 Ex) 2 + 9 + 1 = 2 + 1 + 9 Commutative Property of Multiplication ab = ba Ex) ( 4)(-3) = ( -3)(4) = - 12 Order doesn’t matter.

Associative Property of Addition (a + b) + c = a + ( b + c) Ex) ( 3 + 6) + ( - 4) = 3 + ( 6 + (-4)) 9 + ( -4 ) = 3 + ( 2) 5 = 5 True Because of this property, we can leave off the parentheses when doing Addition.

Associative Property of Multiplication Ex) (ab)c= a(bc)

Is this an example of Commutative or Associative Properties? • Ex) Commutative • I didn’t Regroup, I only rearranged the order inside the Parenthese. • Ex) ( 4 + 9) + 7 = 4 + ( 7 + 9) • Associative and Commutative • I regrouped the numbers and I rearranged the order of the 9 and 7.

Identity Properties Addition Ex) 4 + 0 = 4 a + 0 = a and 0 + a = a Multiplication a( 1) = a and ( 1)a = a Ex) We use this property to find Equivalent Fractions.

Inverse Properties Additive Inverse Ex) 5 + ( -5) = 0 a + ( - a) = 0 Multiplicative Inverse Ex)

Distributive Property a ( b + c ) = ab + ac a ( b – c ) = ab – ac Ex) Verify 3( 9 – 4 ) = 3(9) – 3 (4) 3 ( 5) = 27 – 12 15 = 15

More Examples 6( x + 4) = 6 x + 6(4) = 6 x + 24 - ( 4 x – 8) = - 4 x + 8 8 ( 3 x + 2) + 7 = 8( 3 x) + 8(2) + 7 = 24 x + 16 + 7 = 24 x + 23 5(x) – 5(y) = 5 ( x – y )

Use a Property to Simplify the Expressions • Ex) 9 + ( 13) + ( -9) + 7 • Ex) 2999 + ( 47) + 1 + ( - 7) • Ex) x + (-x ) + (2/3)(3/2) • Ex) 9. 8 x + 7 – 9. 8 x

More Examples • Rewrite each expression using the Distributive Property. 8( x – 5) = 9 x + 9 y + 9 z = - ( 7 x - 2 y + 3 z ) =