Transcript Solve the equation.

Solving
Equations
by by
Solving
Equations
2-2
2-2 Multiplying
or Dividing
Multiplying
or Dividing
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Warm Up
Evaluate each expression.
1. (–7)(2.8) 19.6
2. 0.96 ÷ 6 0.16
3. (–9)(–9) 81
4.
1
5.
2
3
6.
1.8
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Objective
Solve one-step equations in one variable by
using multiplication or division.
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Solving an equation that contains multiplication or
division is similar to solving an equation that
contains addition or subtraction. Use inverse
operations to undo the operations on the variable.
Inverse Operations
Operation
Multiplication
Division
Holt Algebra 1
Inverse Operation
Division
Multiplication
Solving Equations by
2-2 Multiplying or Dividing
Example 1A: Solving Equations by Using
Multiplication
Solve the equation.
j
–8 =
3
–24 = j
Check
Holt Algebra 1
Since j is divided by 3,
multiply both sides by 3
to undo the division.
j
–8 =
3
–24
–8
3
–8 –8 
To check your solution,
substitute –24 for j in the
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Example 1B: Solving Equations by Using
Multiplication
Solve the equation.
n
= 2.8
6
Since n is divided by 6,
multiply both sides by 6
to undo the division.
n = 16.8
n
= 2.8
Check
6
To check your solution,
16.8 2.8
substitute 16.8 for n in the
6
2.8 2.8  original equation.
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 1a
Solve the equation. Check your answer.
p
= 10
5
Since p is divided by 5,
multiply both sides by 5
to undo the division.
p = 50
Check
Holt Algebra 1
p
= 10
5
To check your solution,
50 10
substitute 50 for p in the
5
10 10  original equation.
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 1b
Solve the equation. Check your answer.
y
–13 =
3
Since y is divided by 3,
multiply both sides by 3 to
undo the division.
–39 = y
y
Check –13 =
3
To check your solution,
–39
–13
substitute –39 for y in the
3
–13 –13  original equation.
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 1c
Solve the equation. Check your answer.
c
=7
8
Since c is divided by 8,
multiply both sides by 8
to undo the division.
c = 56
Check
Holt Algebra 1
c
=7
8
56 7
8
7 7
To check your solution,
substitute 56 for c in the
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Example 2A: Solving Equations by Using Division
Solve the equation. Check your answer.
9y = 108
y = 12
Check
9y = 108
9(12)
108
Holt Algebra 1
Since y is multiplied by 9,
divide both sides by 9 to
undo the multiplication.
108 To check your solution,
substitute 12 for y in the
108 
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Example 2B: Solving Equations by Using Division
Solve the equation. Check your answer.
–4.8 = –6v
0.8 = v
Since v is multiplied by –6,
divide both sides by –6 to
undo the multiplication.
Check –4.8 = –6v
–4.8 –6(0.8)
–4.8 –4.8 
Holt Algebra 1
To check your solution,
substitute 0.8 for v in the
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 2a
Solve the equation. Check your answer.
16 = 4c
Since c is multiplied by 4,
divide both sides by 4 to
undo the multiplication.
4=c
Check
16 = 4c
16
16
Holt Algebra 1
4(4)
16 
To check your solution,
substitute 4 for c in the
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 2b
Solve the equation. Check your answer.
0.5y = –10
y = –20
Since y is multiplied by 0.5,
divide both sides by 0.5 to
undo the multiplication.
Check 0.5y = –10
To check your solution,
0.5(–20) –10
–10 –10  substitute –20 for y in the
original equation.
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 2c
Solve the equation. Check your answer.
15k = 75
k=5
Since k is multiplied by 15,
divide both sides by 15 to
undo the multiplication.
Check 15k = 75
15(5)
75
Holt Algebra 1
To check your solution,
75
substitute 5 for k in the
75 
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Remember that dividing is the same as
multiplying by the reciprocal. When
solving equations, you will sometimes
find it easier to multiply by a reciprocal
instead of dividing. This is often true
when an equation contains fractions.
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Example 3A: Solving Equations That Contain
Fractions
Solve the equation.
5
w = 20
6
The reciprocal of 5 is 6 . Since w is
6
5
5
multiplied by , multiply both sides
6
6
by
.
5
w = 24
Check
5
w = 20
6
20
20 20 
Holt Algebra 1
To check your solution,
substitute 24 for w in the
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Example 3B: Solving Equations That Contain
Fractions
Solve the equation.
3
= 1 z
16
8
The reciprocal of 1 is 8. Since z is
8
1
multiplied by , multiply both sides
8
by 8.
3=z
2
3 =1z
Check
16
8
To check your solution,
substitute 3 for z in the
2
original equation.
3
3

16 16
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 3a
Solve the equation. Check your answer.
1
– 1 =
b
5
4
5=b
–4
Check
The reciprocal of 1 is 5. Since b is
5
1
multiplied by , multiply both sides
5
by 5.
1b
1
=
–
4
5

Holt Algebra 1
To check your solution,
substitute – 5 for b in the
4
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 3b
Solve the equation.
4j = 2
3
6
j=1
Holt Algebra 1
4j
is the same as 4 j.
6
6
The reciprocal of 4 is 6 . Since j is
6
4
4
multiplied by , multiply both sides
6
6
by .
4
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 3b Continued
Solve the equation.
4j = 2
3
6
Check
4j = 2
6
3
To check your solution,
substitute 1 for j in the
original equation.

Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Check It Out! Example 3c
Solve the equation.
1
w = 102
6
The reciprocal of 1 is 6. Since w is
6
multiplied by 1 , multiply both sides
6
by 6 .
w = 712
Check
1
w = 102
6
102
102 102 
Holt Algebra 1
To check your solution,
substitute 712 for w in the
original equation.
Solving Equations by
2-2 Multiplying or Dividing
Example 4: Application
Ciro puts 1
4 of the money he earns from mowing
lawns into a college education fund. This year
Ciro added $285 to his college education fund.
Write and solve an equation to find how much
money Ciro earned mowing lawns this year.
one-fourth
times
earnings
equals
college fund
Write an equation to represent the relationship.
Substitute 285 for c. Since m is divided
by 4, multiply both sides by 4 to undo
the division.
m = $1140
Holt Algebra 1
Ciro earned $1140 mowing lawns.
Solving Equations by
2-2 Multiplying or Dividing
Check it Out! Example 4
The distance in miles from the airport that a plane
should begin descending, divided by 3, equals the
plane's height above the ground in thousands of
feet. A plane began descending 45 miles from the
airport. Use the equation to find how high the
plane was flying when the descent began.
Distance
divided by 3
equals
height in thousands of feet
Write an equation to represent the
relationship.
Substitute 45 for d.
15 = h
The plane was flying at 15,000 ft when the descent began.
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Properties of Equality
WORDS
NUMBERS
ALGEBRA
Holt Algebra 1
Addition Property of Equality
You can add the same number to both
sides of an equation, and the statement
will still be true.
3=3
3+2=3+2
5=5
a=b
a+c=b+c
Solving Equations by
2-2 Multiplying or Dividing
Properties of Equality
WORDS
NUMBERS
ALGEBRA
Holt Algebra 1
Subtraction Property of Equality
You can subtract the same number from
both sides of an equation, and the
statement will still be true.
7=7
7–5=7–5
2=2
a=b
a–c=b–c
Solving Equations by
2-2 Multiplying or Dividing
Properties of Equality
WORDS
NUMBERS
ALGEBRA
Holt Algebra 1
Multiplication Property of Equality
You can multiply both sides of an
equation by the same number, and the
statement will still be true.
6=6
6(3) = 6(3)
18 = 18
a=b
ac = bc
Solving Equations by
2-2 Multiplying or Dividing
Properties of Equality
WORDS
Division Property of Equality
You can divide both sides of an equation
by the same nonzero number, and the
statement will still be true.
NUMBERS
8 = 8
8
8
=
4
4
2 =2
ALGEBRA
a=b
(c ≠ 0)
a = a
c
c
Holt Algebra 1
Solving Equations by
2-2 Multiplying or Dividing
Lesson Quiz: Part 1
Solve each equation.
1.
2.
21
2.8
3. 8y = 4
4. 126 = 9q –14
5.
6.
Holt Algebra 1
40
Solving Equations by
2-2 Multiplying or Dividing
Lesson Quiz: Part 2
9
7. A person's weight on Venus is about
his or
10
her weight on Earth. Write and solve an equation
to find how much a person weighs on Earth if he
or she weighs 108 pounds on Venus.
Holt Algebra 1