Simplifying Numerical Expressions By Mr. Schneider

MATHEMATICAL PROPERTIES PART I

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)

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

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

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

ZERO PROPERTY FOR MULTIPLICATION The product of zero and any number is zero Mathematics: 5 • 0 = 0 Algebra: n • 0 = 0

QUICK QUIZ Identify 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

Simplifying Numerical Expressions PART II

(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)

Simplifying Numerical Expressions {(4 • 6) - (4 • 3)} + 15 (Distributive Property) (24 - 12) + 15 (Multiply) 12 + 15 (Combine Terms) (12 + 15) (Associative Property) 27 (Simplified)

Simplifying Numerical Expressions (7 • 4) • 0 (Associative Property) (28 • 0) (Associative Property) 0 (Zero Property)

The End!