Download Algebraic Properties

Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Algebraic Properties
Equations are composed of two expressions set equal to one another. Although the use of
algebra tiles makes it easy to visualize simple equations, the process can get very cumbersome
when solving multiple-step equations. The properties of algebra can be used to simplify
algebraic expressions much more efficiently and applied to solve multiple-step equations.
Property
Properties of Addition and Multiplication
Rule
Example
Commutative of Addition
2+3=3+2
Commutative of
Multiplication
Associative of Addition
2•3=3•2
Associative of
Multiplication
Distributive
(a + b)+c = a(b+c)
(2 + 3)+1 = 2+(3+1)
(a • b)c = a(b • c)
(2 • 3)4 = 2(3•4)
2(x + 5) = 2(x)+2(5) = 2x +
10 or 2x + 10 = 2(x + 5)
The three properties are used to simplify algebraic expressions.
The _________________________________________________ is used to expand groups and
remove parentheses from expressions.
The _________________________________________________ is used to change the order
of the numbers so that like terms are together.
The _________________________________________________ is used to associate or group
like terms.
Sample Problems
Simplify using the algebraic properties.
1. 3(x – 4) – 2(8 – x)
Distributive
Commutative
Associative
Simplified expression
(C) 2012, TESCCC
05/16/12
page 1 of 3
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Algebraic Properties
2. 4(m + n) + 3(2m – 5n)
Distributive
Commutative
Associative
Simplified expression
3. Simplify the expressions and justify each step with the appropriate property.
a. 5(2a + b) – 2(3a – 5b)
b. -2(3p – q) + 5(2p + q)
c. 3(2x – 7) + 6(10x + 5)
d. 4(5x + 1) – (4x – 3)
Expressions can be evaluated by substituting given values for the variables in the expression
and using order of operations.
4. Evaluate the expressions for the given values.
a. 2(3a + b) – (a – 3b), a = 3, b = - 2
b. -2(3x – y) + 5(2x + y), x = -2.2, y = 4.6
c. 3.5(2p – 8q) + 6(2.5p + 5q), p = -1, q = 3
d. 1/4(12m + 2n) – 1/5(5m – 3n), m = 5, n = -10
5. Explain two ways the expressions could be evaluated for the given values.
(C) 2012, TESCCC
05/16/12
page 2 of 3
Algebra 1
HS Mathematics
Unit: 02 Lesson: 01
Algebraic Properties
Practice Problems
1. Simplify the expressions and justify each step with the appropriate property.
a.
-5(4x – 3)
b.
-3x + 5 – 4x – 2
c.
(2x + 5) + 7
d.
2(3x + 7) – (x – 4)
e.
7(2x + 1) – 3(x – 5)
f.
30(1/3m – 3/5n) – 20(3/4m + 2/5n)
2. Evaluate the expressions for the given values.
a. 2p(3m + n) – 3p(5m – 2n); m = 5, p = 1/3, n = 1/2
b. 3.5(x – 1.5y) – 5.5(3x + 6y); x = 2.25, y = -1.2
3. Explain how to use the properties of addition and multiplication to perform the indicated
addition or multiplication mentally in the simplest way.
a. 0.65 + 1.85 + 1.35
b. 425 + 97 + 75
c. 33/5 + 11/8 + 62/5
d. 125 × 798 × 8
e. 2.5 × 6.9 × 4
(C) 2012, TESCCC
05/16/12
page 3 of 3