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

2. Warm Up Evaluate each expression. 1. (–7)(2.8) 2. 0.96 ÷ 6 3. (–9)(–9)4. 5. 6.

3. Objective
Solve one-step equations in one variable by using or .

4. Inverse Operations Operation Inverse Operation
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
Inverse Operation

5. Example 1A: Solving Equations by Using Multiplication
Solve the equation.
–8 = j 3

6. Check It Out! Example 1a
Solve the equation. Check your answer.
= 10 p 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.

7. Check It Out! Example 1b
Solve the equation. Check your answer.
–13 = y 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.

8. Check It Out! Example 1c
Solve the equation. Check your answer.
= 7 c 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.

9. Example 2A: Solving Equations by Using Division
Solve the equation. Check your answer.
9y = 108

10. 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.

11. Check It Out! Example 2a
Solve the equation. Check your answer.
16 = 4c

12. Check It Out! Example 2b
Solve the equation. Check your answer.
0.5y = –10

13. Check It Out! Example 2c
Solve the equation. Check your answer.
15k = 75

14. Remember that dividing is the same as multiplying by the
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 .

15. 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

16. 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
To check your solution, substitute for z in the original equation. 3 2

17. 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
To check your solution, substitute – for b in the original equation. 5 4

18. Check It Out! Example 3b
Solve the equation. = 4j 6 2 3

19. Check It Out! Example 3b Continued
Solve the equation. = 4j 6 2 3

20. Check It Out! Example 3c
Solve the equation. 1
w = 102 6

21. one-fourth times earnings equals college fund
Example 4: Application
Ciro puts 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. 1 4
one-fourth times earnings equals college fund
Write an equation to represent the relationship.

22. Write an equation to represent the relationship.
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.

23. Lesson Quiz: Part 1 1. 2. 3. 8y = 4 4. 126 = 9q 5. 6.
Solve each equation. 1. 2.
3. 8y = 4
= 9q 5. 6.

24. 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