3-8 solving decimal equations homework presentation homework presentation
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3-8 Solving Decimal Equations
Homework PresentationHomework Presentation
3-8 Solving Decimal Equations
Learn to 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
Use inverse operations to get the variable alone on one side of the equation.
Remember!
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 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.
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
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
3-8 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
?
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 is subtracted from n.
Add 3.7 to both sides to undo the subtraction.
+ 3.7 + 3.7
n = 12.3
Check
n – 3.7 = 8.6Substitute 12.3 for n in the equation.12.3 – 3.7 = 8.6
?
8.6 = 8.6?
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
h is multiplied by 7.
Divide both sides by 7 to undo the multiplication.
h = 1.2
Check
7h = 8.4Substitute 1.2 for h in the equation.7(1.2) = 8.4
?
8.4 = 8.4?
1.2 is the solution.
7 7
7h = 8.4
3-8 Solving Decimal Equations
Check It Out: Example 1C
Solve the equation. Check your answer.
= 0.3
= 0.3
w is divided by 9.
Multiply both sides by 9 to undo the division.
w = 2.7
Check
Substitute 2.7 for w in the equation.
0.3 = 0.3?
2.7 is the solution.
· 9
w9
w9
· 9
= 0.3w9
= 0.32.79
?
3-8 Solving Decimal Equations
The area of a rectangle is its length times its width.
A = lw
Remember!
w
l
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?
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.
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?
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.
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?
181.25 = 12.5w
Write the equation for the problem. Let w be the width of the room.
Divide both sides by 12.5 to undo the multiplication.
14.5 = w12.5 12.5
181.25 = 12.5 · w
area = length · width
181.25 = 12.5w
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?
Let C be the total cost. Write the equation for the problem.
Multiply.C = 725
C = 181.25 · 4
total cost = area · cost of carpet per square foot
The cost of carpeting the bedroom is $725.
3-8 Solving Decimal Equations
Check For UnderstandingSolve 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?
x4
3-8 Solving Decimal Equations
1. Solve the equation.
m – 8.7 = 17.8
A. m = 9.1
B. m = 25.5
C. m = 26.5
D. m = 27
Lesson Quiz for Student Response Systems
3-8 Solving Decimal Equations
2. Solve the equation.
A. q = 36.6
B. q = 33.6
C. q = 30.6
D. q = 11.6
Lesson Quiz for Student Response Systems
q 6 = 5.6
3-8 Solving Decimal Equations
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
Lesson Quiz for Student Response Systems
3-8 Solving Decimal Equations
4. Solve the equation.
8u = 73.6
A. u = 5.8
B. u = 9.2
C. u = 65.6
D. u = 81.8
Lesson Quiz for Student Response Systems
3-8 Solving Decimal Equations
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
Lesson Quiz for Student Response Systems
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