Download Simplifying Numerical Expressions

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
 1. Identity
 2. 6(3 + 2) = 6 • 3 + 6 • 2
 2. Distributive
 3. n • 0 = 0
 3. Zero
 4. 55 • 1 = 55
 4. Identity
 5. (a + b) + c = a + (b + c)
 5. Associative
 6. 21 + 0 = 21
 6. Identity
 7. a(b + c) = a • b + a • c
 7. Distributive
 8. 5 • 0 = 0
 8. Zero
 9. 2 + 7 = 7 + 2
 9. Commutative
 10. (3 • 5) • 9 = 3 • (5 • 9)
 10. Associative
 11. 5 • 8 = 8 • 5
 11. Commutative
 12. 5(4 - 1) = 5 • 4 - 5 • 1
 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 - 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)
Simplifying Numerical
Expressions
7•4•0
 (7 • 4) • 0
 (28 • 0)
0
(Numerical Expression)
(Associative Property)
(Associative Property)
(Zero Property)