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PRE-ALGEBRA
Lesson 2-2 Warm-Up
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PRE-ALGEBRA
“The Distributive
Property” (2-2)
What is the
“Distributive
Property”?
The Distributive Property: When multiplying two numbers together, one
can calculate the answer by making one of the numbers into an addition
or subtraction problem in parenthesis, multiplying each of these addend
or subtractands separately by the number outside of the parenthesis, and
adding those “partial products” together.
a (b + c) = ab + ac
Example: 5 (26) = 130
5 (26) = 5 (20 + 6) = 5(20) + 5(6) = 100 + 30 = 130
5 (26) = 5 (25 + 1) = 5(25) + 5(1) = 125 + 5 = 130
a (b - c) = ab - ac
Example: 5 (26) = 130
5 (26) = 5 (30 - 4) = 5(30) - 5(4) = 150 - 20 = 130
5 (26) = 5 (28 - 2) = 5(28) - 5(2) = 140 - 10 = 130
PRE-ALGEBRA
“The Distributive
Property” (2-2)
(b + c)a = ba + ca
Example: 5 (26) = 130
(2 + 3) 26 = 2(26) + 3(26) = 52 + 78 = 130
(4 + 1) 26 = 4(26) + 1(26) = 104 + 26 = 130
(b + c)a = ba + ca
Example: 5 (26) = 130
(10 - 5) 26 = 10(26) - 5(26) = 260 - 130 = 130
(6 - 1) 26 = 6(26) - 1(26) = 156 - 26 = 130
PRE-ALGEBRA
The Distributive Property
LESSON 2-2
Additional Examples
Use the Distributive Property to find 15(110) mentally.
15(110) = 15(100 + 10)
Write 110 as (100 + 10).
= 15 • 100 + 15 • 10
Use the Distributive Property.
= 1,500
Multiply.
=
+
1,650
150
Add.
PRE-ALGEBRA
The Distributive Property
LESSON 2-2
Additional Examples
Ms. Thomas gave 5 pencils to each of her 37 students.
What is the total number of pencils she gave to the students?
(37)5 = (40 – 3)5
= 40 • 5 – 3 • 5
Write 37 as (40 – 3).
Use the Distributive Property.
=
200 – 15
Multiply.
=
185
Subtract.
Ms. Thomas gave the students 185 pencils.
PRE-ALGEBRA
The Distributive Property
LESSON 2-2
Additional Examples
Simplify 11(23) + 11(7).
11(23) + 11(7) = 11(23 + 7)
Use the Distributive Property.
= 11(30)
Work within grouping symbols.
= 330
Multiply.
PRE-ALGEBRA
“The Distributive
Property” (2-2)
How can you model the
Distributive Property?
To model the Distributive Property, model the excpression inside
parenthesis as many times as the number outside the parenthesis. Then,
use the Commutative Property of Addition to regroup the numbers.
Example: Use a model to multiply 3 (2x + 5).
H
3(2x + 5) = 3 • 2x + 3 • 5 = 6x + 15
PRE-ALGEBRA
The Distributive Property
LESSON 2-2
Additional Examples
Use a model to multiply 4(3x – 4).
Model four
groups of
3x – 4.
Use the Commutative
Property of Addition
to regroup.
So 4(3x – 4) = 12x – 16.
PRE-ALGEBRA
The Distributive Property
LESSON 2-2
Additional Examples
Multiply.
a. –9(2 – 8y)
–9(2 – 8y) = –9(2) – (–9)(8y)
Use the Distributive Property.
= –18 – (–72y)
Multiply.
= –18
Simplify.
+ 72y
b. (5m + 6)11
(5m + 6)11 = (5m)11 + (6)11 Use the Distributive Property.
= 55m
+ 66
Multiply.
PRE-ALGEBRA
The Distributive Property
LESSON 2-2
Lesson Quiz
Use the Distributive Property to simplify or solve mentally.
1. 15(203)
3,045
3. 6(26) – 6(16)
60
2. 7(180)
1,260
4. (8a – 4)9
72a – 36
5. 2(14 + y)
28 + 2y
PRE-ALGEBRA