1. Dividing by a number is the inverse of multiplying by that number
Dividing by a number is the inverse of multiplying by that number. To solve an equation that contains multiplication, use division to “undo” the multiplication.
4m = 32
Caution !
4m = 32
4m means “4  m.” 4 4
m = 8

2. Example 1A: Solving Equations by Dividing
Solve the equation. Check your answer.
5p = 75
p is multiplied by 5.
5p = 75
Divide both sides by 5 to undo the multiplication. 5 5
p = 15
Check 5p = 75
5(15)= 75 ?
Substitute 15 for p in the equation.
75 = 75 ? 
15 is the solution.

3. Example 1B: Solving Equations by Dividing
Solve the equation. Check your answer.
16 = 8r
r is multiplied by 8.
16 = 8r
Divide both sides by 8 to undo the multiplication. 8 8
2 = r
Check 16 = 8r
16 = 8(2) ?
Substitute 2 for r in the equation.
16 = 16 ? 
2 is the solution.

4. Solve the equation. Check your answer.
Check It Out! Example 1A
Solve the equation. Check your answer.
8a = 72
a is multiplied by 8.
8a = 72
Divide both sides by 8 to undo the multiplication. 8 8
a = 9
Check 8a = 72
8(9)= 72 ?
Substitute 9 for a in the equation.
72 = 72 ? 
9 is the solution.

5. Solve the equation. Check your answer.
Check It Out! Example 1B
Solve the equation. Check your answer.
18 = 3w
w is multiplied by 3.
18 = 3w
Divide both sides by 3 to undo the multiplication. 3 3
6 = w
Check 18 = 3w
18 = 3(6) ?
Substitute 6 for w in the equation.
18 = 18 ? 
6 is the solution.

6. Example 2: Problem Solving Application
The area of a rectangle is 56 square inches. Its length is 8 inches. What is its width?
Remember!
For a rectangle, area = length  width

7. Understand the Problem
Example 2 Continued 1
Understand the Problem
The answer will be the width of the rectangle in inches.
List the important information:
The area of the rectangle is 56 square inches.
The length of the rectangle is 8 inches.
Draw a diagram to represent this information. w 56 8

8. Example 2 Continued 2
Make a Plan
You can write and solve an equation using the formula for area. To find the area of a rectangle, multiply its length by its width.
A = lw w
56 = 8w l

9. So the width of the rectangle is 7 inches.
Example 2 Continued
Solve 3
56 = 8w
w is multiplied by 8.
56 = 8w
Divide both sides by 8 to undo the multiplication. 8 8
7 = w
So the width of the rectangle is 7 inches.

10. Example 2 Continued 4
Look Back
Arrange 56 identical squares in a rectangle. The length is 8, so line up the squares in rows of 8. You can make 7 rows of 8, so the width of the rectangle is 7.

11. Check It Out! Example 2
The area of a rectangle is 48 square inches. Its width is 8 inches. What is its length?

12. Understand the Problem
Check It Out! Example 2 Continued 1
Understand the Problem
The answer will be the length of the rectangle in inches.
List the important information:
The area of the rectangle is 48 square inches.
The width of the rectangle is 8 inches.
Draw a diagram to represent this information. 48 8 l

13. Check It Out! Example 2 Continued
Make a Plan
You can write and solve an equation using the formula for area. To find the area of a rectangle, multiply its length by its width.
A = lw w
48 = l8 l

14. Check It Out! Example 2 Continued
Solve 3
48 = 8l
l is multiplied by 8.
48 = 8l
Divide both sides by 8 to undo the multiplication. 8 8
6 = l
So the length of the rectangle is 6 inches.

15. Check It Out! Example 2 Continued4
Look Back
Arrange 48 identical squares in a rectangle. The width is 8, so line up the squares in columns of 8. You can make 6 columns of 8, so the length of the rectangle is 6.