3-8 Solving Decimal Equations
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
3-8 Solving Decimal Equations
Warm Up
Solve.
1. x – 3 = 11
x = 14
2. 18 = x + 4
x = 14
3. x = 42
x = 294
4. 2x = 52
x = 26
5. x – 82 = 172
x = 254
7
3-8 Solving Decimal Equations
Problem of the Day
Find the missing entries in the magic
square. 11.25 is the sum of every row,
column, and diagonal.
3
6.75 1.5
2.25 3.75 5.25
6
0.75 4.5
3-8 Solving Decimal Equations
I can solve equations involving decimals.
3-8 Solving Decimal Equations
You can solve equations with decimals
using inverse operations just as you
solved equations with whole numbers.
$45.20 + m = $69.95
–$45.20
–$45.20
m = $24.75
3-8 Solving Decimal Equations
Remember!
Use inverse operations to get the variable
alone on one side of the equation.
3-8 Solving Decimal Equations
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 + 6.2
k = 15.7
Check
k – 6.2 = 9.5
?
15.7 – 6.2 = 9.5
?
9.5 = 9.5 
6.2 is subtracted from k.
Add 6.2 to both sides to
undo the subtraction.
Substitute 15.7 for k in
the equation.
15.7 is the solution.
3-8 Solving Decimal Equations
Additional Example 1B: Solving One-Step
Equations with Decimals
Solve the equation. Check your answer.
6k = 7.2
6k = 7.2
6k = 7.2
6
6
k = 1.2
k is multiplied by 6.
Divide both sides by 6 to
undo the multiplication.
Check
6k = 7.2
?
6(1.2) = 7.2
?
7.2 = 7.2 
Substitute 1.2 for k in
the equation.
1.2 is the solution.
3-8 Solving Decimal Equations
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
Multiply both sides by 7
· 7 = 0.6 · 7
7
to undo the division.
m = 4.2
Check
m
= 0.6
7
4.2 ?
= 0.6
7
?
0.6 = 0.6 
Substitute 4.2 for m in
the equation.
4.2 is the solution.
3-8 Solving Decimal Equations
Check It Out: Example 1A
Solve the equation. Check your answer.
n – 3.7 = 8.6
n – 3.7 = 8.6
+ 3.7 + 3.7
n = 12.3
Check
n – 3.7 = 8.6
?
12.3 – 3.7 = 8.6
?
8.6 = 8.6 
3.7 is subtracted from n.
Add 3.7 to both sides to
undo the subtraction.
Substitute 12.3 for n in
the equation.
12.3 is the solution.
3-8 Solving Decimal Equations
Check It Out: Example 1B
Solve the equation. Check your answer.
7h = 8.4
7h = 8.4
7h = 8.4
7
7
h = 1.2
h is multiplied by 7.
Divide both sides by 7 to
undo the multiplication.
Check
7h = 8.4
?
7(1.2) = 8.4
?
8.4 = 8.4 
Substitute 1.2 for h in
the equation.
1.2 is the solution.
3-8 Solving Decimal Equations
Check It Out: Example 1C
Solve the equation. Check your answer.
w
= 0.3
9
w
· 9 = 0.3 · 9
9
w = 2.7
Check
w
= 0.3
9
2.7 ?
= 0.3
9
?
0.3 = 0.3 
w is divided by 9.
Multiply both sides by 9
to undo the division.
Substitute 2.7 for w in
the equation.
2.7 is the solution.
3-8 Solving Decimal Equations
Remember!
The area of a rectangle is its length times
its width.
w
l
A = lw
3-8 Solving Decimal Equations
Additional Example 2A: Measurement Application
The area of Emily’s floor is 33.75 m2. If its
length is 4.5 meters, what is its width?
area = length · width
33.75 = 4.5 · w
33.75 = 4.5w
Write the equation for the problem.
Let w be the width of the room.
33.75 = 4.5w
4.5
4.5
7.5 = w
Divide both sides by 4.5 to
undo the multiplication.
The width of Emily’s floor is 7.5 meters.
3-8 Solving Decimal Equations
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
C = 33.75 · 23 Let C be the total cost. Write the
equation for the problem.
C = 776.25
Multiply.
The cost of carpeting the floor is $776.25.
3-8 Solving Decimal Equations
Check It Out: Example 2A
The area of Yvonne’s bedroom is 181.25 ft2. If
its length is 12.5 feet, what is its width?
area = length · width
181.25 = 12.5 · w
181.25 = 12.5w
Write the equation for the problem.
Let w be the width of the room.
181.25 = 12.5w
12.5
12.5
14.5 = w
Divide both sides by 12.5 to
undo the multiplication.
The width of Yvonne’s bedroom is 14.5 feet.
3-8 Solving Decimal Equations
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
C = 181.25 · 4 Let C be the total cost. Write the
equation for the problem.
C = 725
Multiply.
The cost of carpeting the bedroom is $725.
3-8 Solving Decimal Equations
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
3-8 Solving Decimal Equations
Lesson Quiz
Solve each equation. Check your answer.
1. x – 3.9 = 14.2
x = 18.1
2. x = 8.3
4
3. x – 4.9 = 16.2
x = 33.2
4. 7x = 47.6
x = 6.8
x = 21.1
5. The area of the floor in Devon’s room is 35.7 m2.
If the width is 4.2 m, what is the length of the
bedroom?
8.5 m
3-8 Solving Decimal Equations
Lesson Quiz for Student Response Systems
1. Solve the equation.
m – 8.7 = 17.8
A. m = 9.1
B. m = 25.5
C. m = 26.5
D. m = 27
3-8 Solving Decimal Equations
Lesson Quiz for Student Response Systems
2. Solve the equation.
q
= 5.6
6
A. q = 36.6
B. q = 33.6
C. q = 30.6
D. q = 11.6
3-8 Solving Decimal Equations
Lesson Quiz for Student Response Systems
3. Solve the equation.
s – 9.9 = 18.7
A. s = 28.6
B. s = 27.9
C. s = 27.7
D. s = 8.8
3-8 Solving Decimal Equations
Lesson Quiz for Student Response Systems
4. Solve the equation.
8u = 73.6
A. u = 5.8
B. u = 9.2
C. u = 65.6
D. u = 81.8
3-8 Solving Decimal Equations
Lesson Quiz for Student Response Systems
5. Laura bought 9.7 yards of fabric for
$76.63. What is the cost per yard?
A. $9.90
B. $9.70
C. $7.90
D. $7.70