Solving
Equations
by by
Solving
Equations
Multiplying
or Dividing
Multiplying
or Dividing
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal
Algebra 1 Algebra 1
Solving Equations by
Multiplying or Dividing
Warm Up
Evaluate each expression.
1. (–7)(2.8)
2. 0.96 ÷ 6
3. (–9)(–9)
4.
5.
6.
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Objective
Solve one-step equations in one variable by
using
or
.
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Solving an equation that contains
or
is similar to solving an equation that
contains
or
. Use inverse
operations to undo the operations on the
.
Inverse Operations
Operation
Holt McDougal Algebra 1
Inverse Operation
Solving Equations by
Multiplying or Dividing
Example 1A: Solving Equations by Using
Multiplication
Solve the equation.
j
–8 =
3
Holt McDougal Algebra 1
Solving Equations by
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.
To check your solution,
substitute 50 for p in the
original equation.
Holt McDougal Algebra 1
Solving Equations by
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.
To check your solution,
substitute –39 for y in the
original equation.
Holt McDougal Algebra 1
Solving Equations by
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.
To check your solution,
substitute 56 for c in the
original equation.
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Example 2A: Solving Equations by Using Division
Solve the equation. Check your answer.
9y = 108
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Example 2B: Solving Equations by Using Division
Solve the equation. Check your answer.
–4.8 = –6v
Holt McDougal Algebra 1
Since v is multiplied by –6,
divide both sides by –6 to
undo the multiplication.
Solving Equations by
Multiplying or Dividing
Check It Out! Example 2a
Solve the equation. Check your answer.
16 = 4c
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Check It Out! Example 2b
Solve the equation. Check your answer.
0.5y = –10
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Check It Out! Example 2c
Solve the equation. Check your answer.
15k = 75
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Remember that dividing is the same as
multiplying by the
. When
solving equations, you will sometimes
find it easier to
by a
instead of
. This is often true
when an equation contains
.
Holt McDougal Algebra 1
Solving Equations by
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
Holt McDougal Algebra 1
Solving Equations by
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.
To check your solution,
substitute 3 for z in the
2
original equation.
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Check It Out! Example 3a
Solve the equation. Check your answer.
1
– 1 =
b
5
4
The reciprocal of 1 is 5. Since b is
5
1
multiplied by , multiply both sides
5
by 5.
To check your solution,
substitute – 5 for b in the
4
original equation.
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Check It Out! Example 3b
Solve the equation.
4j = 2
3
6
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Check It Out! Example 3b Continued
Solve the equation.
4j = 2
3
6
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Check It Out! Example 3c
Solve the equation.
1
w = 102
6
Holt McDougal Algebra 1
Solving Equations by
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.
Holt McDougal Algebra 1
Solving Equations by
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.
Holt McDougal Algebra 1
Solving Equations by
Multiplying or Dividing
Lesson Quiz: Part 1
Solve each equation.
1.
2.
3. 8y = 4
4. 126 = 9q
5.
6.
Holt McDougal Algebra 1
Solving Equations by
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 McDougal Algebra 1