Page 78 - Algebra 1

L E S S O N Using the Properties of Real Numbers to
12
Simplify Expressions
Warm Up
New Concepts
1. Vocabulary A(n) expression is an expression with constants
(9)
and/or variables that uses the operations +, -, ×, or ÷. 2. Simplify 6 - ⎪-6⎥ + (-4).
(5)
3.Divide-_4 ÷(-_8). (11) 5 9
4. Evaluate 2⎪y⎥ - 2⎪x⎥ + m for x = -1.5, y = -3, and m = -1.3. (9)
The properties of real numbers are used to simplify expressions and write equivalent expressions. The table shows properties of addition and multiplication when a, b, and c are real numbers.
Properties of Addition and Multiplication
Identity Property of Addition
For every real number a,
a + 0 = a Example: 5 + 0 = 5
Identity Property of Multiplication
For every real number a,
a · 1 = a Example: 5 · 1 = 5
Commutative Property of Addition
For every real number a and b,
a + b = b + a Example: 5 + 2 = 2 + 5
7=7
Commutative Property of Multiplication
For every real number a and b,
a · b = b · a Example: 5 · 2 = 2 · 5
ab = ba 10 = 10
Associative Property of Addition
For every real number a, b, and c,
(a + b) + c = a + (b + c) Example: (1 + 2) + 3 = 1 + (2 + 3)
a+b+c=a+b+c 3+3=1+5 6=6
Associative Property of Multiplication
For every real number a, b, and c,
(a · b) · c = a · (b · c) Example: (1 · 2) · 3 = 1 · (2 · 3)
abc = abc 2 · 3 = 1 · 6 6=6
Math Language
0 is the additive identity.
1 is the multiplicative identity.
Online Connection www.SaxonMathResources.com
Lesson 12 63