Simplifying Numerical Expressions

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Simplifying Numerical Expressions

• By
• Mr. Schneider

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MATHEMATICALPROPERTIES

• PART I

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ASSOCIATIVE PROPERTY

• Addition Changing the grouping of the addends
  does not change the sum.
• Mathematics (56 22) 6 56 (22 6)
  Algebra (a b) c a
  (b c)
• Multiplication Changing the grouping of the
  factors does not change the product.
• Mathematics(3 5) 9 3 (5 9)
  Algebra (a b) c a (b c)

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COMMUTATIVE PROPERTY

• Addition Changing the order of the addends does
  not change the sum.
• Mathematics 2 7 7 2
• Algebra a b b a
• Multiplication Changing the order of the factors
  does not change the product.
• Mathematics 5 8 8 5
  Algebra a b b a

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IDENTITY PRPOERTY

• Addition Adding zero does not change the sum.
• Mathematics 21 0 21 Algebra n 0 n
• Multiplication Multiplying any number by 1 does
  not change the product.
• Mathematics 55 1 55 Algebra n 1 n

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DISTRIBUTIVE PROPERTY FOR MULTIPICATION

• You can multiply each term inside a set of
  parentheses by a factor outside of the
  parentheses.
• Mathematics 6(3 2) 6 3 6 2 Algebra
  a(b c) a b a c
• Mathematics 5(4 - 1) 5 4 - 5 1
  Algebra a(b - c) a b - a c

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ZERO PROPERTY FOR MULTIPLICATION

• The product of zero and any number is zero
• Mathematics 5 0 0
  Algebra n 0 0

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QUICK QUIZIdentify each of the properties
(Associative, Commutative, Distributive,
Identity, or Zero)

• 1. 17 0 17
• 2. 6(3 2) 6 3 6 2
• 3. n 0 0
• 4. 55 1 55
• 5. (a b) c a (b c)
• 6. 21 0 21
• 7. a(b c) a b a c
• 8. 5 0 0
• 9. 2 7 7 2
• 10. (3 5) 9 3 (5 9)
• 11. 5 8 8 5
• 12. 5(4 - 1) 5 4 - 5 1

• 1. Identity
• 2. Distributive
• 3. Zero
• 4. Identity
• 5. Associative
• 6. Identity
• 7. Distributive
• 8. Zero
• 9. Commutative
• 10. Associative
• 11. Commutative
• 12. Distributive

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Simplifying Numerical Expressions

• PART II

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(Numerical Expression)

• Simplifying numerical expressions allows you to
  combine like terms to make the mathematics
  easier. You use the properties to do the
  simplifications.
• 27 32 13 18 (Numerical Expression)
• 27 13 32 18 (Commutative Property)
• (27 13) ( 32 18) (Associative Property)
• 40 50 (Combine Terms)
• 90 (Simplified)

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Simplifying Numerical Expressions

• 4(6 - 3) 15 (Numerical Expression)
• (4 6) - (4 3) 15 (Distributive Property)
• (24 - 12) 15 (Multiply)
• 12 15 (Combine Terms)
• (12 15) (Associative Property)
• 27 (Simplified)

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Simplifying Numerical Expressions

• 7 4 0 (Numerical Expression)
• (7 4) 0 (Associative Property)
• (28 0) (Associative Property)
• 0 (Zero Property)

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The End!