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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)

Today’s Learning Goal Assignment

Learn to solve equations involving decimals.

Course 1

3-10 Solving Decimal Equations

6th Grade Math HW

Page 136

#9-20 allCourse 1



Course 1

Warm upWarm up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpSolve.

1. x – 3 = 11

2. 18 = x + 4

3. = 42

4. 2x = 52

5. x – 82 = 172

x = 14

Course 1


x7

x = 14

x = 294

x = 26

x = 254

Problem of the Day

Find the missing entries in the magic square. 11.25 is the sum of every row, column, and diagonal.

3

Course 1


3.75 5.25

6

6.75 1.5

2.25

0.75 4.5

Today’s Learning Goal Assignment

Learn to solve equations involving decimals.

Course 1


Course 1


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


Use inverse operations to get the variable alone on one side of the equation.

Remember!

Course 1


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 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


Additional Example 1B: Solving One-Step Equations with Decimals

Solve the equation. Check your answer.B. 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?


6 6

6k = 7.2

Course 1


Additional Example 1C: Solving One-Step Equations with Decimals


C. = 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?


· 7

m7

m7

· 7

= 0.6m7

= 0.64.27

?

Course 1


Try This: Example 1A


A. 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?


Course 1


Try This: Example 1B


B. 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?


7 7

7h = 8.4

Course 1


Try This: Example 1C


C. = 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?


· 9

w9

w9

· 9

= 0.3w9

= 0.32.79

?

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The area of a rectangle is its length times its width.

A = lw

Remember!

w

l

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Additional Example 2A: Measurement Application


A. 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


Additional Example 2B: Measurement Application


B. 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.

Course 1


Try This: Example 2A


A. 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.

Course 1


Try This: Example 2B


B. 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.

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


x4

x = 18.1

x = 33.2

x = 21.1

x = 6.8

8.5 m

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