1. Lesson Objective: I will be able to …
Solve one-step equations in one variable by
using multiplication or division
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

2. 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

3. Example 1: Solving Equations by Using Multiplication
Page 10
Solve each equation. Check your answer. j 3
= 2.8 n 6 B.
A. –8 =
Since j is divided by 3, multiply both sides by 3 to undo the division.
Since n is divided by 6, multiply both sides by 6 to undo the division.
–24 = j
n = 16.8
Check
–8 = j 3
Check
= 2.8 n 6 –8
–24 3
2.8
16.8 6
–8 –8  

4. Solve the equation. Check your answer.
Your Turn 1
Page 10
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 y
Check
–13 = 3
To check your solution, substitute –39 for y in the original equation.
–13
–39 3
–13 –13 

5. Example 2: Solving Equations by Using Division
Page 11
Solve each equation. Check your answer.
A. 9y = 108
B. –4.8 = –6v
Since y is multiplied by 9, divide both sides by 9 to undo the multiplication.
Since v is multiplied by –6, divide both sides by –6 to undo the multiplication.
y = 12
0.8 = v
Check 9y = 108
Check –4.8 = –6v
–4.8 –6(0.8)
9(12) 108
–4.8 –4.8  

6. Solve the equation. Check your answer.
Your Turn 2
Page 11
Solve the equation. Check your answer.
15k = 75
Since k is multiplied by 15, divide both sides by 15 to undo the multiplication.
k = 5
Check 15k = 75
To check your solution, substitute 5 for k in the original equation.
15(5) 75 

7. 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.

8. Example 3: Solving Equations That Contain Fractions
Page 12
Solve each equation. Check your answer. 5 16 1 8
= z 3 B.
A w = -20 6
The reciprocal of is 8. Since z is multiplied by , multiply both sides by 8. 1 8
The reciprocal of is Since w is multiplied by , multiply both sides by 5 6
= z 3 2
Check 1 8 3 16
= z
w = -24
Check
w = 20 5 6
20 16 3
20 20  

9. Solve the equation. Check your answer. 1 4 1 5 – = b
Your Turn 3
Page 12
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 

10. Example 4: Economic Application
Page 13
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.

11. Page 9

12. Classwork
Assignment #4
Holt 2-2 #4-10, 42, 53, 57