Download 1.7 Algebra I Notes ~ Distributive Property Date

1.7 Algebra I Notes ~ Distributive Property
Date: _____________________
Ex. Calculate the following expressions:
a) 3(4 + 5)
b) 3(4) + 3(5)
How are the two problems above related?
The Distributive Property
For every real number a, b, and c,
Simplifying an expression
Ex. Use the distributive property to simplify the following:
a) 3(4m – 7)
b) –3(n – 4)
c) ( 6x − 3) (−2)
d)
e) ( 3q + 10 ) 0.5
f) ( 7 − 2r )
1
(12 − 4t)
4
5
21
Using the Multiplication Property of –1
a) –(5q – 6)
b) –(9 + x)
Vocabulary
A number, a variable, or the product of a number and one or more variables
A term that has no variable
A numerical factor of a term
Terms that have exactly the same variable factors
Ex. 6a 2 − 5ab + 3b − 12
Combining like terms
a) –2w2 + w2
b) a − 5a
c) −15x 2 + 27x 2
d) xy − 3xy
e) 7m + n
1.8 Algebra I Notes ~ Properties of Real Numbers
Date: _________________
Properties of Real Numbers
Let a, b, and c represent real numbers.
Property
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Identity Property of Addition
Identity Property of Multiplication
Inverse Property of Addition
Inverse Property of Multiplication
Distributive Property
Multiplication Property of Zero
Multiplication Property of –1
Example
Ex. Name the property that each equation illustrates:
a) 3 ⋅ a = a ⋅ 3
c) −
b) (6) + (–6) = 0
3
3
+0=−
4
4
d) (–1 + 2) + 3 = –1 + (2 + 3)
e) 4(6 ⋅17) = (4 ⋅ 6) ⋅17
f) 3(7 – 4) = 3(7) – 3(4)
g) 35 + 2 = 2 + 35
1
h) − ⋅ (−3) = 1
3
i) −0.25 ⋅ ( −4 ) = 1
Justifying Steps
Ex. Give a reason to justify each step:
a) 3x + 2(5 + x) + (x ⋅ 4) = 3x + 10 + 2x + (x ⋅ 4)
b)
= 5x + 10 + 2x + (4 ⋅ x)
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c)
= 7x + 10 + 6x
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d)
= 10 + 7x + 6x
e)
= 10 + 13x
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f)
= 13x + 10
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