Download Week two notes

Lesson
3.3
Lesson Tutorials
Expressions with the same value, like 12 + 7 and 7 + 12, are equivalent
expressions. You can use the Commutative and Associative Properties to
write equivalent expressions.
Key Vocabulary
equivalent
expressions, p. 128
Commutative Properties
Changing the order of addends or factors does not change the
sum or product.
Words
Numbers
5+8=8+5
⋅
Algebra
⋅
a+b=b+a
⋅
5 8=8 5
⋅
a b=b a
Associative Properties
Changing the grouping of addends or factors does not change
the sum or product.
Words
Numbers
(7 + 4) + 2 = 7 + (4 + 2)
⋅ ⋅
⋅ ⋅
(7 4) 2 = 7 (4 2)
Algebra
(a + b) + c = a + (b + c)
⋅ ⋅
⋅ ⋅
(a b) c = a (b c)
EXAMPLE
1
Using Properties to Write Equivalent Expressions
a. Simplify the expression 7 + (12 + x).
Study Tip
7 + (12 + x) = (7 + 12) + x
One way to check
whether expressions are
equivalent is to evaluate
each expression for any
value of the variable. In
Example 1(a), use x = 2.
7 + (12 + x) = 19 + x
= 19 + x
21 = 21
✓
Add 7 and 12.
b. Simplify the expression (6.1 + x) + 8.4.
(6.1 + x) + 8.4 = (x + 6.1) + 8.4
?
7 + (12 + 2) = 19 + 2
Associative Property of Addition
Commutative Property of Addition
= x + (6.1 + 8.4)
Associative Property of Addition
= x + 14.5
Add 6.1 and 8.4.
c. Simplify the expression 5(11y).
⋅
5(11y) = (5 11)y
Associative Property of Multiplication
= 55y
Multiply 5 and 11.
Simplify the expression. Explain each step.
Exercises 5 – 8
128
Chapter 3
ms_green pe_0303.indd 128
1. 10 + (a + 9)
2.
( )
2
3
1
2
c+— +—
3.
5(4n)
Algebraic Expressions and Properties
1/28/15 1:32:08 PM
Lesson
3.4
Lesson Tutorials
Key Vocabulary
like terms, p. 136
Distributive Property
Words
To multiply a sum or difference by a number, multiply each
number in the sum or difference by the number outside the
parentheses. Then evaluate.
Numbers
3(7 + 2) = 3 × 7 + 3 × 2
a(b + c) = ab + ac
Algebra
3(7 − 2) = 3 × 7 − 3 × 2
EXAMPLE
1
a(b − c) = ab − ac
Using Mental Math
Use the Distributive Property and mental math to find 8 × 53.
8 × 53 = 8(50 + 3)
EXAMPLE
2
Write 53 as 50 + 3.
= 8(50) + 8(3)
Distributive Property
= 400 + 24
Multiply.
= 424
Add.
Using the Distributive Property
1
2
3
4
Use the Distributive Property to find — × 2 —.
1
2
3
4
( )
( ) ( )
1
2
3
4
3
4
1
2
1
2
3
4
Rewrite 2 — as the sum 2 + —.
— × 2— = — × 2 + —
3
4
= —×2 + —×—
Distributive Property
3
8
=1+—
Multiply.
3
8
= 1—
Add.
Use the Distributive Property to find the product.
Exercises 5 –16
1. 5 × 41
2.
9 × 19
3.
6(37)
1
2
5.
— × 4—
1
5
6.
— × 3—
2
3
4. — × 1—
134
Chapter 3
ms_green pe_0304.indd 134
1
4
2
7
3
4
Algebraic Expressions and Properties
1/28/15 1:33:37 PM