1. Learn to solve equations involving decimals.

2. You can solve equations with decimals using inverse operations just as you solved equations with whole numbers.
$ m = $69.95
–$45.20
–$45.20
m = $24.75

3. Use inverse operations to get the variable alone on one side of the equation.
Remember!

4. Additional Example 1A: Solving One-Step Equations with Decimals
Solve the equation. Check your answer.
k – 6.2 = 9.5
k – 6.2 = 9.5
6.2 is subtracted from k.
+ 6.2
+ 6.2
Add 6.2 to both sides to undo the subtraction.
k = 15.7
Check
k – 6.2 = 9.5
Substitute 15.7 for k in the equation.
15.7 – 6.2 = 9.5 ?
9.5 = 9.5 ? 
15.7 is the solution.

5. Additional Example 1B: Solving One-Step Equations with Decimals
Solve the equation. Check your answer.
6k = 7.2
k is multiplied by 6.
6k = 7.2
6k = 7.2
Divide both sides by 6 to undo the multiplication. 6 6
k = 1.2
Check
6k = 7.2
Substitute 1.2 for k in the equation.
6(1.2) = 7.2 ?
7.2 = 7.2 ? 
1.2 is the solution.

6. Additional Example 1C: Solving One-Step Equations with Decimals
Solve the equation. Check your answer. m
= 0.6
m is divided by 7. 7 m 7
· 7
= 0.6
· 7
Multiply both sides by 7 to undo the division.
m = 4.2
Check
= 0.6 m 7
Substitute 4.2 for m in the equation.
= 0.6
4.2 7 ?
0.6 = 0.6 ? 
4.2 is the solution.

7. Solve the equation. Check your answer.
Check It Out: Example 1A
Solve the equation. Check your answer.
n – 3.7 = 8.6
n – 3.7 = 8.6
3.7 is subtracted from n.
+ 3.7
+ 3.7
Add 3.7 to both sides to undo the subtraction.
n = 12.3
Check
n – 3.7 = 8.6
Substitute 12.3 for n in the equation.
12.3 – 3.7 = 8.6 ?
8.6 = 8.6 ? 
12.3 is the solution.

8. Solve the equation. Check your answer.
Check It Out: Example 1B
Solve the equation. Check your answer.
7h = 8.4
h is multiplied by 7.
7h = 8.4
7h = 8.4
Divide both sides by 7 to undo the multiplication. 7 7
h = 1.2
Check
7h = 8.4
Substitute 1.2 for h in the equation.
7(1.2) = 8.4 ?
8.4 = 8.4 ? 
1.2 is the solution.

9. Solve the equation. Check your answer.
Check It Out: Example 1C
Solve the equation. Check your answer. w
= 0.3
w is divided by 9. 9 w 9
· 9
= 0.3
· 9
Multiply both sides by 9 to undo the division.
w = 2.7
Check
= 0.3 w 9
Substitute 2.7 for w in the equation.
= 0.3
2.7 9 ?
0.3 = 0.3 ? 
2.7 is the solution.

10. The area of a rectangle is its length times its width.
A = lw
Remember! w l

11. Additional Example 2A: Measurement Application
The area of Emily’s floor is m2. If its length is 4.5 meters, what is its width?
area = length · width
33.75 = 4.5 · w
Write the equation for the problem. Let w be the width of the room.
33.75 = 4.5w
33.75 = 4.5w
Divide both sides by 4.5 to undo the multiplication.
4.5
4.5
7.5 = w
The width of Emily’s floor is 7.5 meters.

12. Additional Example 2B: Measurement Application
If carpet costs $23 per square meter, what is the total cost to carpet the floor?
total cost = area · cost of carpet per square meter
Let C be the total cost. Write the equation for the problem.
C = · 23
C =
Multiply.
The cost of carpeting the floor is $

13. Check It Out: Example 2A
The area of Yvonne’s bedroom is ft2. If its length is 12.5 feet, what is its width?
area = length · width
= 12.5 · w
Write the equation for the problem. Let w be the width of the room.
= 12.5w
= 12.5w
Divide both sides by 12.5 to undo the multiplication.
12.5
12.5
14.5 = w
The width of Yvonne’s bedroom is 14.5 feet.

14. Check It Out: Example 2B
If carpet costs $4 per square foot, what is the total cost to carpet the bedroom?
total cost = area · cost of carpet per square foot
Let C be the total cost. Write the equation for the problem.
C = · 4
C = 725
Multiply.
The cost of carpeting the bedroom is $725.