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3-9 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
Course 1
3-9 Solving Decimal Equations
Learn to solve equations involving
decimals.
Course 1
3-9 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
Course 1
3-9 Solving Decimal Equations
Remember!
Use inverse operations to get the variable
alone on one side of the equation.
Course 1
3-9 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 
Course 1
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.
3-9 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 
Course 1
Substitute 1.2 for k in
the equation.
1.2 is the solution.
3-9 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 
Course 1
Substitute 4.2 for m in
the equation.
4.2 is the solution.
3-9 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.
Course 1
3-9 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.
Course 1
3-9 Solving
Insert Decimal
Lesson Equations
Title Here
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
Course 1
Solving Fraction Equations:
5-10 Multiplication and Division
Learn to solve equations by multiplying
and dividing fractions.
Course 1
Solving Fraction Equations:
5-10 Multiplication and Division
Remember!
Dividing by a number is the same as multiplying
by its reciprocal.
Course 1
Solving Fraction Equations:
5-10 Multiplication and Division
Additional Example 1A: Solving Equations by
Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
3
__
j = 25
5
3
3
3
__
j ÷ __ = 25 ÷ __
5
5
5
3
Divide both sides of the equation by __ .
5
3
__
j•
5
3
5
Multiply by __, the reciprocal of __.
5
3
5
5
__
__
= 25 •
3
3
5
j = 25 • __
3
25 • 5
j = _____
1•3
125
2
j = ___, or 41 __
3
3
Course 1
Solving Fraction Equations:
5-10 Multiplication and Division
Additional Example 1B: Solving Equations by
Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
2
7x = __
5
1
2
7x
1
__ • __
= __ • __
7
5
1
7
Multiply both sides by the reciprocal
of 7.
2•1
x = ____
5•7
2
__
x=
35
Course 1
The answer is in simplest form.
Solving Fraction Equations:
5-10 Multiplication and Division
Additional Example 1C: Solving Equations by
Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
5y
__ = 6
8
5
6
5y
5
__
__ ÷ __
__
=
÷
8
1
8
8
5
__
Divide both sides by 8 .
8
6
5y
8
__ • __
= __ • __
5
1
8
5
5
__
Multiply by the reciprocal of
.
8
48
3
y = __ , or 9 __
5
5
Course 1
Solving Fraction Equations:
5-10 Multiplication and Division
Check It Out: Example 1A
Solve each equation. Write the answer in simplest form.
3
__
j = 19
4
3
3
3
__
j ÷ __ = 19 ÷ __
4
4
4
3
Divide both sides of the equation by __ .
4
3
__
j•
4
3
4
Multiply by __, the reciprocal of __.
4
3
4
4
__
__
= 19 •
3
3
4
j = 19 • __
3
19 • 4
j = _____
1•3
76
1
___
j=
, or 25 __
3
3
Course 1
Solving Fraction Equations:
5-10 Multiplication and Division
Check It Out: Example 1B
Solve each equation. Write the answer in simplest form.
1
3x = __
7
1
1
3x
1
__ • __
= __ • __
3
7
1
3
Multiply both sides by the reciprocal
of 3.
1•1
x = ____
7•3
1
x = __
21
Course 1
The answer is in simplest form.
Solving Fraction Equations:
5-10 Multiplication and Division
Lesson Quiz
Solve each equation. Write the answer in
simplest form.
1
1
1. 3x = __
x = __
8
24
1 x=4
2. __
x = 16
4
3 x = 14
__
y =9
2 4. __
3. __
x = 98 or 32 __
7
7
3
3
y = 63
1 of the
5. Rebecca used 3 pt of paint to paint __
4
trim in her bedroom. How many pints will Rebecca
use for the trim in the entire bedroom? 12
Course 1