1. Simplifying Numerical ExpressionsBy
Mr. Schneider

2. MATHEMATICAL PROPERTIES
PART I

3. 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)

4. 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

5. 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

6. 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

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

8. 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

9. Simplifying Numerical Expressions
PART II

10. (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)

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

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

13. The End!