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**Simplifying Numerical Expressions**

By Mr. Schneider

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**MATHEMATICAL PROPERTIES**

PART I

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ASSOCIATIVE PROPERTY Addition: Changing the grouping of the addends does not change the sum. Mathematics: ( ) + 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: = 7 + 2 Algebra: a + b = b + a Multiplication: Changing the order of the factors does not change the product. Mathematics: 5 • 8 = 8 • Algebra: a • b = b • a

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**IDENTITY PRPOERTY Addition: Adding zero does not change the sum.**

Mathematics: = Algebra: n + 0 = n Multiplication: Multiplying any number by 1 does not change the product. Mathematics: 55 • 1 = 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 • • 2 Algebra: a(b + c) = a • b + a • c Mathematics: 5(4 - 1) = 5 • • 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 = Algebra: n • 0 = 0

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QUICK QUIZ Identify each of the properties (Associative, Commutative, Distributive, Identity, or Zero) = 17 2. 6(3 + 2) = 6 • • 2 3. n • 0 = 0 4. 55 • 1 = 55 5. (a + b) + c = a + (b + c) = 21 7. a(b + c) = a • b + a • c 8. 5 • 0 = 0 = 7 + 2 10. (3 • 5) • 9 = 3 • (5 • 9) 11. 5 • 8 = 8 • 5 12. 5(4 - 1) = 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. (Numerical Expression) (Commutative Property) ( ) +( ) (Associative Property) (Combine Terms) 90 (Simplified)

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**Simplifying Numerical Expressions**

{(4 • 6) - (4 • 3)} + 15 (Distributive Property) ( ) (Multiply) (Combine Terms) ( ) (Associative Property) 27 (Simplified)

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**Simplifying Numerical Expressions**

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

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The End!

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