Download Mathematics 8 Notes - Canal Winchester High School

Algebra 1 Notes
Warm Up
1.
12.4
If y = 16, y – 3.6 = ____
16 – 3.6
2.
59
45 – (- 14) = ___
3.
36  4(2)
2
14
= ____
14
4. -3 + 17 = ____
GOAL
USE THE DIST. PROP. TO EVALUATE/SIMPLIFY EXPRESSIONS; RECOGNIZE
AND USE THE COMMUTATIVE AND ASSOCIATIVE PROP.; FIND SQUARE
ROOTS; CLASSIFY AND ORDER REAL NUMBERS.
KEY WORDS & PROPERTIES
COEFFICIENT, EQUIVALENT EXPRESSIONS, IRRATIONAL NUMBERS, LIKE
TERMS, PERFECT SQUARE, PRINCIPAL SQUARE ROOT, RADICAL SIGN,
RATIONAL APPROXIMATION, REAL NUMBERS, SIMPLEST FORM, SQUARE
ROOT, TERM,
Properties
• Commutative
Order of the terms does not change your answer
3+5=5+3
a+b=b+a
4*3=3*4
• Associative
• Distributive
• Identity
x*y=y*x
Moving grouping symbols does not
change your answer
3 + (5 + 7) = (3 + 5) + 7
(6 * 5) * 9 = 6 * (5 * 9)
a + (b + c) = (a + b) + c
a * (b * c) = (a * b) * c
Multiply your outside term times all terms inside
the parentheses
a(b + c) = ab + ac
5(7 + 9) = 5(7) + 5(9)
Of Addition: 3 + 0 = 3
Of Multiplication: 5 * 1 = 5
x+0=x
x*1=x
Example 1
Use the Distributive Property to simplify the expressions.
3(2x + 6)
5(6m + 4n – 3n)
3(2x)  3(6)
5(6m )  5(4n)  5(3n)
6x  18
30 m  20 n  15 n
30 m  5n
Example 2
Use the distributive property to write this product in another way.
1
18( 2 )
9
1
18(2)  18( )
9
36  2
38
Example 3
Simplify by collecting like terms.
3
3
4a  6a  3a  8a
3
3
4a  3a  6a  8a
7a3  14a
Example 4
Simplify.
3.2(x + y) + 2.3(x + y) + 4x
3.2x  3.2y  2.3x  2.3y  4x
3.2x  2.3x  4x  3.2y  2.3y
9.5x  5.5y
Example 5
Evaluate.
 94
 9.695