1. Multiplying or Dividing 1-3
Solving Equations by
Multiplying or Dividing
1-3
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1
Holt Algebra 1

2. Objective
Solve one-step equations in one variable by using multiplication or division.

3. Inverse Operations Operation Inverse Operation
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
Inverse Operation
Multiplication
Division
Division
Multiplication

4. Example 1A: Solving Equations by Using Multiplication
Solve the equation.
–8 = j 3
Since j is divided by 3, multiply both sides by 3 to undo the division.
–24 = j
Check
–8 = j 3 –8
–24 3
To check your solution, substitute –24 for j in the original equation.
–8 –8 

5. Example 1B: Solving Equations by Using Multiplication
Solve the equation.
= 2.8 n 6
Since n is divided by 6, multiply both sides by 6 to undo the division.
n = 16.8
Check
= 2.8 n 6
2.8
16.8 6
To check your solution, substitute 16.8 for n in the original equation. 

6. Example 2A: Solving Equations by Using Division
Solve the equation. Check your answer.
9y = 108
Since y is multiplied by 9, divide both sides by 9 to undo the multiplication.
y = 12
Check 9y = 108
To check your solution, substitute 12 for y in the original equation.
9(12) 108 

7. Example 2B: Solving Equations by Using Division
Solve the equation. Check your answer.
–4.8 = –6v
Since v is multiplied by –6, divide both sides by –6 to undo the multiplication.
0.8 = v
Check –4.8 = –6v
–4.8 –6(0.8)
To check your solution, substitute 0.8 for v in the original equation.
–4.8 –4.8 

8. Check It Out! Example 2b
Solve the equation. Check your answer.
0.5y = –10
Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication.
y = –20
Check 0.5y = –10
0.5(–20) –10
To check your solution, substitute –20 for y in the original equation.
–10 –10 

9. Example 3A: Solving Equations That Contain Fractions
Solve the equation. 5
w = 20 6
The reciprocal of is Since w is multiplied by , multiply both sides by 5 6
w = 24
Check
w = 20 5 6
To check your solution, substitute 24 for w in the original equation.
20
20 20 

10. Example 3B: Solving Equations That Contain Fractions
Solve the equation. 3 1 8
= z 16
The reciprocal of is 8. Since z is multiplied by , multiply both sides by 8. 1 8
= z 3 2
Check 1 8 3 16
= z
To check your solution, substitute for z in the original equation. 3 2 3 16 

11. Solve the equation. Check your answer. 1 4 1 5 – = b
Check It Out! Example 3a
Solve the equation. Check your answer. 1 4 1 5
– = b
The reciprocal of is 5. Since b is multiplied by , multiply both sides by 5. 1 5
= b 5 4 –
= b 5 4
Check 1 –
To check your solution, substitute – for b in the original equation. 5 4 

12. To check your solution, substitute 712 for w in the original equation.
Check It Out! Example 3c
Solve the equation. 1
w = 102 6
The reciprocal of is 6. Since w is multiplied by , multiply both sides by 6 . 1 6
w = 712
Check
w = 102 1 6
102
To check your solution, substitute 712 for w in the original equation. 

13. Lesson Quiz: Part 2
7. A person's weight on Venus is about his or 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. 9 10