Transcript Slide 1

Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Homework # 7 – Word Problems
pg 92 # 51
An investor purchases 50 shares of a stock at $3.50 per
share. The next day, the change in value of a share of the
stock is -$0.25. What is the total value of the shares the next
day?
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.5 – Apply the Distributive Property
Example # 1
Find the total areas of the two rectangles modeled below.
Area of Rectangle = Length * Width
Area # 1 = Length * Width
Area # 1 = 7 units * x units
Area # 1 = 7x units
Rectangle
#1
7 units
Rectangle 7 units
#2
Area # 2 = Length * Width
Area # 2 = 7 units * 3 units
Area # 2 = 21 units
x units
Total Area of the Rectangles = Area # 1 + Area # 2
Total Area of the Rectangles = 7x units + 21 units
Total Area of the Rectangles = 7x + 21 units
3 units
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.5 – Apply the Distributive Property
Example # 1 (con’t)
Find the area of the rectangle modeled below.
Rectangle
Area of Rectangle = Length * Width
Area of Rectangle = Length * Width
Area of Rectangle = 7 units *( x + 3 ) units
7 units
Area of Rectangle = ((7 * x) + (7 * 3))units
Area of Rectangle = 7x + 21 units
Note:
Total Area of the Rectangles = 7x + 21 units
x + 3 units
Thus; Total Area of the Rectangles = Area of Rectangle
The Distributive Property allows you to find the product of a number with a
sum/difference expression.
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.5 – Apply the Distributive Property
Examples
Distributive Property
Given
Distributive
Step
The product of a and (b + c) a(b + c) = ab + ac
4(3+5)
= 4(3) + 4(5)
= 12 + 20 = 32
(b + c)a = ba + ca
(3+5)4
= (3)4 + (5)4
= 12 + 20 = 32
4(x+5)
= 4(x) + 4(5)
= 4x + 20
a(b - c) = ab - ac
6(3-5)
= 6(3) - 6(5)
= 18 - 30 = -12
(b - c)a = ba - ca
(3-5)6
= (3)6 - (5)6
= 18 - 30 = -12
4(x-2)
= 4(x) - 4(2)
= 4x - 8
Words
The product of a and (b - c)
Algebra
Answer
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.5 – Apply the Distributive Property
Example # 2
Use the distributive property to write an equivalent expression.
a) (y – 2) * (-4)
Distribute -4
(y)*(-4) – (2)*(-4) Multiply
b) -5x * (4 - x)
(-5x)*(4) – (-5x)*(x) Multiply
-4y – (-8)
Add the opposite of - 8 -20x – (-5x2)
-4y + 8
Simplified Expression
c) -(3y – 9)
Distribute -5x
-20x + 5x2
Distribute -1
(-1)*(3y) – (-1)*(9)
Multiply
-3y – (-9)
Add the opposite of - 9
-3y + 9
Simplified Expression
Add the opposite of -5x2
Simplified Expression
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.5 – Apply the Distributive Property
Terms – the parts of the expression that are added together
Coefficient – the number part of a term with a variable part
Constant – the number part of expression that does not contain a variable
Like Terms – are terms that have the same variable parts
Example # 3
Identify the terms, like terms, coefficients, and constant terms of the following expression
a) -2x – 8 + 6x + 5
Like Terms: -2x, 6x; -8, +5;
Coefficients: -2, +6
Constant Terms: -8, +5
Coefficients: 3, -8
Constant Terms: 6, -2
Coefficients: -5, 3
Constant Terms: 6, 6
b) 3y + 6 – 8y – 2
Like Terms: 3y, -8y; +6, -2
c) 6 - 5x + 3y + 6
Like Terms: 6, 6;
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.5 – Apply the Distributive Property
PROBLEM SOLVING PLAN
STEP 1 : READ AND UNDERSTAND
Read the Problem CAREFULLY!!!
Identify Variables and Constants.
What is the problem asking?
STEP 2 : ORGANIZE YOUR THOUGHTS
Formulate an Approach.
Make an equation, inequality or expression.
STEP 3 : SOLVE THE PROBLEM
Evaluate the equation, inequality or expression
STEP 4 : CHECK YOUR WORK
DOES IT MAKES SENSE!!!
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.5 – Apply the Distributive Property
Example # 3
You are making curtains by alternating strips of solid colored fabric
and patterned fabric. The solid colored fabric costs $0.99 per strip and
the patterned fabric costs $1.25 per strip. You need 7 strips for one
curtain. Find the total cost if you use 3 solid colored strips.
Write a verbal model.
Total Cost for Curtain
Cost for
w/ 3 Solid
= Solid Colored
Colored Strips
Strips
Number of
Cost for
Number of
* Solid Colored + Patterned Colored * Patterned Colored
Strips
Strips
Strips
(strips)
(dollars per strips)
(strips)
(dollars per strips)
(dollars)
Write an Equation.
C
=
($0.99)
*
S
+
($1.25)
*
(7 – S)
C = ($0.99)* S + ($1.25) * (7 – S)
Distribute $1.25
C = $0.99S + ($1.25)(7) - ($1.25)(S)
Multiply
C = $0.99S + $8.75 - $1.25S
Combine Like Terms
C = $8.75 - $0.26S
Simplified Equation
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.5 – Apply the Distributive Property
Example # 3 (con’t)
You are making curtains by alternating strips of solid colored fabric and
patterned fabric. The solid colored fabric costs $0.99 per strip and the patterned
fabric costs $1.25 per strip. You need 7 strips for one curtain. Find the total cost
if you use 3 solid colored strips.
Find the Total Cost (C) when the number of colored strips (S) = 3.
Substitute
C = $8.75 - $0.26(3)
Multiply
C = $8.75 - $0.78
Add
C = $7.97
The total cost if you use 3 solid colored fabric strips to make a curtain is $ 7.97.
Chapter 2 – Properties of Real Numbers
Algebra I A - Meeting 9
Section 2.6 – Divide Real Numbers
Inverse Property of Multiplication
The product of a nonzero number and its multiplicative inverse is 1.
a
1
1

 a  1, a  0
a
a
Division Rule
To divide a number a by a nonzero number b, multiply a by the multiplicative
inverse of b.
1
a b  a
Example # 4
a)
8
1
1
8
b
,b  0
b) 5  2  5 
1
2
The Sign of a Quotient The quotient of two real numbers with the same sign is positive.
The quotient of two real numbers with different signs is negative.
The quotient of 0 and any nonzero real numbers is 0.
Chapter 2 – Properties of Real Numbers
Section 2.6 – Divide Real Numbers
Example # 5
Simplify the following expression.
a) 40 x  32
8
Rewrite the fraction as division
=
Apply the division rule
=
Use the Distributive Property
=
Simplify
=
Algebra I A - Meeting 9
Chapter 2 – Properties of Real Numbers
Section 2.5, 2.6
Homework # 8
pg 99 # 3 – 42 mult. of 3; # 53
pg 106 # 9 – 23 odd; # 33 – 43 odd
Algebra I A - Meeting 9