Download CHAPTER 3:

LORD MAY THY WILL BE DONE IN ALL THINGS. 
CHAPTER 2:
Solving Equations
NAME: _______________________
PERIOD: _____
SECTION: 2.1 Properties and Operations
Objective: TLW use properties of addition and multiplication.
Standards: M7.A.2.1, M7.A.2.1.1, M7.A.3.2, M7.A.3.2.1,
M7.B.1.1, M7.B.1.1.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Perimeter:
Triangle
Square
P=
Rectangle
P=
P=
Area of a Square or Rectangle:
Square
Rectangle
A=
A=
Area of a Triangle:
Triangle
A=
Commutative Property of
Addition
Commutative Property of
Multiplication
Words: In a sum, you can add the numbers Words: In a product, you can multiply the
in any order.
numbers in any order.
Numbers:
Numbers:
Algebra:
Algebra:
Assocative Property of Addition
Associative Property of
Multiplication
Words: Changing the grouping of the
numbers in a sum does not change the sum.
Words: Changing the grouping of the numbers
in a product does not change the product.
Numbers:
Numbers:
Algebra:
Algebra:
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1:
You buy a portable CD player for $48, rechargeable batteries with charger
for $25, and a CD case for $12. Find the total cost.
Example 1 You try: Mental Math
a. 32 + 16 + 8
b. (15)(-9)(2)
c. 4(20) (25)(-5)
*****************************************************************
Example 2: Evaluate 4xy when x = -7 and y = 25.
Example 2 You try:
Evaluate the following expressions when a = 9 and b = -4.
a.
b(25a 2 )
b. 11  4b  a
2
c. 3a  b  13
*****************************************************************
Identity Property of Addition
Identity Property of Multiplication
Words: The sum of a number and the
additive identity, 0, is the number.
Words: The product of a number and the
multiplicative identity, 1, is the number.
Numbers:
Numbers:
Algebra:
Algebra:
Example 3: Identifying Properties
Statement
a. (-5)(1) = -5
b. 2 + (-9) = -9 + 2
Property Illustrated
2
2
c. y  0  y
d. 2(pq) = (2p)q
*****************************************************************
Unit Analysis: Conversion factors are used to convert measurements into
different units.
*****************************************************************
Example 4: The Steel Dragon 2000 is one of the world’s longest roller
coaster. Its length is 2711 yards. How long is the roller coaster in feet?
Example 4 You try:
One type of fish eaten by swordfish is the mackerel. A swordfish
can grow to a length of about 5 yards, while the length of an adult
mackerel is about 18 inches.
? feet ? inches
5
yards

5
yards


a. Copy and complete:
1yard 1 foot
b. Use properties of multiplication to evaluate the product in part
(a). What is the length of a swordfish in inches?
c. A swordfish is how many times as long as a mackerel?
HOMEWORK:
SECTION: 2.2 The Distributive Property
Objective: TLW use the distributive property.
Standards: M7.A.3.2, M7.A.3.2.1, M7.B.2.1, M7.B.2.1.3
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: You and your friend are going on a camping trip. You each buy
a backpack that costs $90 and a sleeping bag that costs $60. What is
the total cost of the camping equipment?
Method 1:
Method 2:
The Distributive Property:
Algebra: a(b + c) = ab + ac
(b + c)a = ba + ca
a(b – c) = ab – ac
(b – c)a = ba - ca
Numbers:
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 2: Use the distribute property to evaluate the expression.
a. 5(7 + 2)
b. -3(9 – 1)
c. (11 – 3)4
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 3: Use the distributive property to write an equivalent variable
expression.
a. 8(x + 2)
b.
9(m + 5)
c. (7 – t)(-4)
d. 2(x + 6)
e. 5(4k + 9)
g. (2u – 7)u
h. -3y(y + 8)
f. -4(2n – 7)
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 4: Find the area of the rectangle or triangle.
Example 4 You try:
a.
HOMEWORK:
b.
c.
SECTION: 2.3 Simplifying Variable Expressions
Objective: TLW simplify variable expressions.
Standards: M7.A.3.2, M7.A.3.2.1, M7.B.2.1, M7.B.2.1.3
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
Terms:
5x + 4x + 7
Coefficient:
Constant Term:
Like Terms:
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Identify the terms, like terms, coefficients, and constant
terms of the expression y + 8 – 5y - 3.
Terms:
Like terms:
Coefficients:
Constant Terms:
***A variable expression is simplified if it contains no grouping symbols
and all like terms are combined.***
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 2: Simplify the expression 4n – 7 – n + 9.
Examples 1 and 2 You Try:
a.
6x  x  2  4
terms:
like terms:
coefficients:
constant terms:
b.  4k  12  3k
c. 5n  1  n  8
terms:
like terms:
coefficients:
constant terms:
terms:
like terms:
coefficients:
constant terms:
Example 3: Simplifying Expressions with Parentheses.
a. 2( x  4)  9 x  1
b. 3k  8(k  2)
c. 4a  (4a  3)
d. 5 x  3( x  1)
e.
f. p  6( p  2)
 7(2r  3)  11r
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 4: Write and simplify an expression for the perimeter of the
triangle or rectangle.
a.
HOMEWORK:
b.
c.
EXTRA INFORMATION: Rates and Unit Rates
Objective: TLW understand rates and unit rates.
Standards: M7.D.2.1, M7.D.2.1.1, M7.D.2.2, M7.D.2.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
rate:
unit rate:
a. 45 miles per hour
b. $3 per square foot
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: At a grocery store, the price of bananas is $1.19 per pound.
What is the cost of 3 pounds of bananas?
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 2: You fill a pool with water at a rate of 20 gallons per minute.
Write an expression for the volume of water in the pool
after t minutes.
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 3: DISTANCE FORMULA: d = rt
An ocean liner travels at a constant speed of 36 miles per hour. How far does the ocean liner
travel in 4.5 hours?
HOMEWORK:
SECTION: 2.4 Variables and Equations
Objective: TLW solve equations with variables.
Standards: M7.D.2.1, M7.D.2.1.1, M7.D.2.2, M7.D.2.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
Equation:
Solution:
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Writing Verbal Sentences as Equations
a. The
b. The
c. The
d. The
sum of x and 6 is 9.
difference of 12 and y is 15.
product of -4 and p is 32.
quotient of n and 2 is 9.
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 2: Tell whether 9 or 7 is solution of x – 5 = 2.
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 3: The perimeter of the figure shown is 35 centimeters.
a. Write an equation that you can use to find x.
b. Solve your equation. What is the value of x?
HOMEWORK:
SECTION: 2.5 Solving Equations Using Addition or Subtraction
Objective: TLW solve equations using addition or subtraction
Standards: M7.D.2.1, M7.D.2.1.1, M7.D.2.2, M7.D.2.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
Inverse operations:
Equivalent equations:
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
SUBTRACTION PROPERTY OF EQUALITY
Words:
Subtracting the same number from each side of an equation
produces an equivalent equation.
Numbers:
Algebra:
Example 1: Solve the following equations using subtraction.
a. x  9  3
b.
c. a  8  20
d.  5  17  y
Example 1 You try:
a. n + 1 = 5
b. 0 = r + 32
x  4  10
ADDITION PROPERTY OF EQUALITY
Words:
Adding the same number from each side of an equation
produces an equivalent equation.
Numbers:
Algebra:
Example 2: Solve the following equations using addition.
a. n  4  11
b.
c. 177  403  w
d. t  32  15
Example 1 You try:
a. -5 + s = 4
26  p  61
b. n – 2 – 15 = 4
Example 3: Find the value of x for the given triangle or rectangle.
a. Perimeter = 34 in.
HOMEWORK:
b. Perimeter = 300 ft
SECTION: 2.6 Solving Equations Using Multiplication and Division
Objective: TLW solve equations using multiplication and division.
Standards: M7.D.2.1, M7.D.2.1.1, M7.D.2.2, M7.D.2.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
DIVISION PROPERTY OF EQUALITY
Words: Dividing each side of an equation by the same nonzero
number produces an equivalent equation.
Algebra:
Numbers:
Example 1: Solve the following equations using division.
a.
 6x  48
b.
3x  27
c.
 4(9 g )  252
d.
 23a  0
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1 You try:
a.
3x  24
b.
 110  10 y
MULTIPLICATION PROPERTY OF EQUALITY
Words:
Numbers:
Algebra:
Multiplying the same number from each side of an equation
produces an equivalent equation.
Example 2: Solve the following equations using multiplication.
a. 9 
w
7
c.  8 
b
8
b.
d.
y
 13
2
w
 9  (4)
8
Example 2 You try:
a.
c
 91
2
b.  3 
z
6  11
Example 3: The figure shown is composed of a triangle and a rectangle.
a. Write and simplify an expression in terms of x for the area of the
figure.
b. What is the value of x if the area of the figure is 154 square feet?
HOMEWORK:
SECTION: 2.7 Decimal Operations and Equations with Decimals
Objective: TLW solve equations involving decimals.
Standards: M7.A.3.2, M7.A.3.2.1, M7.D.2.1, M.D.2.1.1,
M7.D.2.2, M7.D.2.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Adding and subtracting decimals
a.
 2.9  (6.5)
b.
 25.38  (42.734)
c.
 1.3  (4.2)
d.
9.817  (1.49)
Example 2: Multiplying and dividing decimals.
a.
 0.7(18.4)
b.
 4.5(9.25)
c.
 29.07  (1.9)
d.
16.83  (3.3)
b.
0.8(3  11n)  1.4n
Example 3: Simplify the expression.
a.
2.6x  7.1x
Example 4: Solve the equation.
a.
x  4.7  3.5
b.
y  6.91  2.26
c.
 1.8u  6.3
d.
y
 0.4
11.5
HOMEWORK: