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Properties of Real Numbers

Learn about properties of real numbers such as commutative, associative, identity, and inverse properties. Discover how to simplify algebraic expressions using these properties and the distributive property in this comprehensive guide.

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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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