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

5. 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.
–39 = y

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

7. 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

8. Remember that dividing is the same as multiplying by the reciprocal
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.

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

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

11. 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.
Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division.
m = $1140
Ciro earned $1140 mowing lawns.

12. Properties of Equality 3 = 3 3 + 2 = 3 + 2 5 = 5 a = b a + c = b + c
WORDS
Addition Property of Equality
You can add the same number to both sides of an equation, and the statement will still be true.
NUMBERS
3 = 3
3 + 2 = 3 + 2
5 = 5
ALGEBRA
a = b
a + c = b + c

13. Properties of Equality 7 = 7 7 – 5 = 7 – 5 2 = 2 a = b a – c = b – c
WORDS
Subtraction Property of Equality
You can subtract the same number from both sides of an equation, and the statement will still be true.
NUMBERS
7 = 7
7 – 5 = 7 – 5
2 = 2
ALGEBRA
a = b
a – c = b – c

14. Properties of Equality 6 = 6 6(3) = 6(3) 18 = 18 a = b ac = bc
WORDS
Multiplication Property of Equality
You can multiply both sides of an equation by the same number, and the statement will still be true.
NUMBERS
6 = 6
6(3) = 6(3)
18 = 18
ALGEBRA
a = b
ac = bc

15. Properties of Equality
Division Property of Equality
You can divide both sides of an equation by the same nonzero number, and the statement will still be true.
WORDS
a = b
(c ≠ 0)
8 = 8
2 = 2
ALGEBRA
NUMBERS 8 4 = a c

16. Lesson Quiz: Part 1 1. 2. 21 3. 8y = 4 4. 126 = 9q 2.8 5. 6. –14 40
Solve each equation. 1. 2.
3. 8y = 4
= 9q 5. 6. 21
2.8
–14 40

17. 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