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Properties of Real Numbers

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.

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Properties of Real Numbers

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  1. 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.

  2. 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.

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

  4. 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.

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

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

  7. 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

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

  9. 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) 9.8x + 7 – 7 – 9.8x

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

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