Transcript 3-10

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Student Progress Chart
Lesson Reflection
3-10
Math Learning Goal
Students will
understand
decimals.
Students will understand decimals by being
able to do the following:
• Learn to write, compare, and order decimals using place value and
number lines (3-1)
• Learn to estimate decimal sums, differences, products, and quotients (3-2)
• Learn to add and subtract decimals (3-3)
• Learn to multiply and divide decimals by powers of ten and to convert
metric measurements (3-4)
• Learn to write large numbers in scientific notation (3-5)
• Learn to multiply decimals by whole numbers and by decimals (3-6)
• Learn to divide decimals by whole numbers (3-7)
• Learn to divide whole numbers and decimals by decimals (3-8)
• Learn to solve problems by interpreting the quotient (3-9)
• Learn to solve equations
involving decimals (3-10)
3-10 Solving Decimal Equations
Today’s Learning Goal Assignment
Learn to solve
equations
involving
decimals.
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3-10 Solving Decimal Equations
th
6
Grade Math HW
Page 136
#9-20 all
Course 1
3-10 Solving Decimal Equations
Warm up
Problem of the Day
Lesson Presentation
Course 1
3-10 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
3-10 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
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0.75 4.5
3-10 Solving Decimal Equations
Today’s Learning Goal Assignment
Learn to solve
equations
involving
decimals.
Course 1
3-10 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
3-10 Solving Decimal Equations
Remember!
Use inverse operations to get the variable
alone on one side of the equation.
Course 1
3-10 Solving Decimal Equations
Additional Example 1A: Solving One-Step
Equations with Decimals
Solve the equation. Check your answer.
A. 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.
3-10 Solving Decimal Equations
Additional Example 1B: Solving One-Step
Equations with Decimals
Solve the equation. Check your answer.
B. 6k = 7.2
k is multiplied by 6.
6k = 7.2
Divide both sides by 6 to
6k = 7.2
undo the multiplication.
6
6
k = 1.2
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.
3-10 Solving Decimal Equations
Additional Example 1C: Solving One-Step
Equations with Decimals
Solve the equation. Check your answer.
m
C.
= 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.
3-10 Solving Decimal Equations
Try This: Example 1A
Solve the equation. Check your answer.
A. 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 
Course 1
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.
3-10 Solving Decimal Equations
Try This: Example 1B
Solve the equation. Check your answer.
B. 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 
Course 1
Substitute 1.2 for h in
the equation.
1.2 is the solution.
3-10 Solving Decimal Equations
Try This: Example 1C
Solve the equation. Check your answer.
w
C.
= 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 
Course 1
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.
3-10 Solving Decimal Equations
Remember!
The area of a rectangle is its length times
its width.
w
l
A = lw
Course 1
3-10 Solving Decimal Equations
Additional Example 2A: Measurement Application
Solve the equation. Check your answer.
A. 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
3-10 Solving Decimal Equations
Additional Example 2B: Measurement Application
Solve the equation. Check your answer.
B. 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.
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3-10 Solving Decimal Equations
Try This: Example 2A
Solve the equation. Check your answer.
A. 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.
Course 1
3-10 Solving Decimal Equations
Try This: Example 2B
Solve the equation. Check your answer.
B. 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.
Course 1
3-10 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