Warm UpSolve.
1. x – 3 = 11
2. 18 = x + 4
3. = 42
4. 2x = 52
5. x – 82 = 172
x = 14
Course 1
3-9 Solving Decimal Equations
x7
x = 14
x = 294
x = 26
x = 254
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
Use inverse operations to get the variable alone on one side of the equation.
Remember!
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 is subtracted from k.
Add 6.2 to both sides to undo the subtraction.
+ 6.2 + 6.2
k = 15.7
Check
k – 6.2 = 9.5Substitute 15.7 for k in the equation.15.7 – 6.2 = 9.5
?
9.5 = 9.5?
15.7 is the solution.
Course 1
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
k is multiplied by 6.
Divide both sides by 6 to undo the multiplication.
k = 1.2
Check
6k = 7.2Substitute 1.2 for k in the equation.6(1.2) = 7.2
?
7.2 = 7.2?
1.2 is the solution.
6 6
6k = 7.2
Course 1
3-9 Solving Decimal Equations
Additional Example 1C: Solving One-Step Equations with Decimals
Solve the equation. Check your answer.
= 0.6
= 0.6
m is divided by 7.
Multiply both sides by 7 to undo the division.
m = 4.2
Check
Substitute 4.2 for m in the equation.
0.6 = 0.6?
4.2 is the solution.
· 7
m7
m7
· 7
= 0.6m7
= 0.64.27
?
Course 1
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?
33.75 = 4.5w
Write the equation for the problem. Let w be the width of the room.
Divide both sides by 4.5 to undo the multiplication.
7.5 = w4.5 4.5
33.75 = 4.5 · w
area = length · width
33.75 = 4.5w
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?
Let C be the total cost. Write the equation for the problem.
Multiply.C = 776.25
C = 33.75 · 23
total cost = area · cost of carpet per square meter
The cost of carpeting the floor is $776.25.
Lesson QuizSolve each equation. Check your answer.
1. x – 3.9 = 14.2
2. = 8.3
3. x – 4.9 = 16.2
4. 7x = 47.6
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?
Insert Lesson Title Here
Course 1
3-9 Solving Decimal Equations
x4
x = 18.1
x = 33.2
x = 21.1
x = 6.8
8.5 m
Course 1
5-10Solving Fraction Equations: Multiplication and Division
Learn to solve equations by multiplying and dividing fractions.
Course 1
5-10Solving Fraction Equations: Multiplication and Division
Dividing by a number is the same as multiplying by its reciprocal.
Remember!
Course 1
5-10Solving Fraction Equations: Multiplication and DivisionAdditional Example 1A: Solving Equations by
Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
j = 25 35__
j ÷ = 25 ÷ 35__ 3
5__ 3
5__
j • = 25 • 35__ 5
3__ 5
3__
j = 25 • 51 • 3_____
j = 25 • 53__
j = , or 41125
3___ 2
3__
Divide both sides of the equation by .
35__
Multiply by , the reciprocal of .
35__5
3__
Course 1
5-10Solving Fraction Equations: Multiplication and Division
Additional Example 1B: Solving Equations by Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
7x = 25__
7x1__ 2
5__ 1
7__1
7__• = •
x =
2 • 15 • 7____
x =
235__
Multiply both sides by the reciprocal of 7.
The answer is in simplest form.
Course 1
5-10Solving Fraction Equations: Multiplication and Division
Additional Example 1C: Solving Equations by Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
= 65y8__
5y8__ 6
1__ 5
8__5
8__÷ = ÷
y = , or 9 485__
Divide both sides by .
58__
5y8__ 6
1__ 8
5__8
5__• = •
35__
58Multiply by the reciprocal of .
__
Course 1
5-10Solving Fraction Equations: Multiplication and Division
Check It Out: Example 1A
Solve each equation. Write the answer in simplest form.
j = 19 34__
j ÷ = 19 ÷ 34__ 3
4__ 3
4__
j • = 19 • __3
4__ 4
343__
j = 19 • 41 • 3_____
4j = 19 • 3__
76___ 13
j = , or 253
__
Divide both sides of the equation by .
34__
Multiply by , the reciprocal of .
34__4
3__
Course 1
5-10Solving Fraction Equations: Multiplication and Division
Check It Out: Example 1B
Solve each equation. Write the answer in simplest form.
3x = 17__
3x1__ 1
7__ 1
3__1
3__• = •
x =
1 • 17 • 3____
x =
121__
Multiply both sides by the reciprocal of 3.
The answer is in simplest form.
Course 1
5-10Solving Fraction Equations: Multiplication and Division
Lesson QuizSolve each equation. Write the answer in simplest form.
1. 3x = 2. x = 4
3. x = 14 4. = 9
5. Rebecca used 3 pt of paint to paint of the
trim in her bedroom. How many pints will Rebecca
use for the trim in the entire bedroom?
18__ 1
4__
37__ y
7__
14__
x = 16124__x =
983__ 2
3__x = or 32 y = 63
12