3-8 solving equations containing fractions warm up warm up lesson presentation lesson presentation...

3-8 Solving Equations Containing Fractions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpSolve.

1. x – 16 = 8

2. 7a = 35

3.

4. y + 21 = 31

x = 24

a = 5

x = 132x12

= 11

y = 10


Problem of the Day

Write 15 positive integers less than 1,000 with digits that, when added together, total 4.

4, 13, 22, 31, 40, 103, 112, 121, 130, 202, 211, 220, 310, 400


Learn to solve one-step equations that contain fractions.


Gold classified as 24 karat is pure gold, while gold classified as 18 karat is only pure. 3

4

14

The remaining of 18-karat gold is

made up of one or more different metals, such as silver, copper, or zinc. The color of gold varies, depending on the type and amount of each metal added to the pure gold.


Equations can help you determine the amounts of metals in different kinds of gold. The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to isolate the variable on one side of the equation.


Solve. Write the answer in simplest form.

Additional Example 1A: Solving Equations by Adding or Subtracting

x – 37

= 57

x – 37

= 57

x – 37

+ 37

= 57

+ 37

Use the Addition Property of Equality.

x = 87

=1 17

Add.



Additional Example 1B: Solving Equations by Adding or Subtracting

49

+ r = -1 2

49

+ r = -1 2

49

+ r – 49

= -1 2

– 49

Use the Subtraction Property of Equality.

r = -918

– 818

r = – 1718

Find a common denominator.

Subtract.

You can also isolate the variable r by adding the opposite of

Helpful Hint

49

, – 49

, to both sides.



Check It Out: Example 1A

x – 38

= 78

x – 38

= 78

x – 38

+ 38

= 78

+ 38

Use the Addition Property of Equality.

x = 10 8

= 1 14

Simplify.



Check It Out: Example 1B

314

+ t = – 27

314

+ t = – 27

Use the Subtraction Property of Equality.

Find a common denominator.

Subtract.

314

+ t – = – 27

–3

143

14

t = – – 314

414

t = – 714

Simplify.t = – 1 2


Solve. Write the answer in simplest terms.

Additional Example 2A: Solving Equations by Multiplying

38

x = 14

38

x =. 83

14

. 83

2

1

=x 23

Multiply by the reciprocal of .38

Then simplify.

38

= 14

x =

To undo multiplying by

Caution!38

, you can divide by 38

or multiply by its reciprocal, 83

.


Additional Example 2B: Solving Equations by Multiplying

4x = 89

89

x =. 14

89

. 141

2

x = 29

4x =

4

Multiply by the reciprocal of 4.

Then simplify.




Check It Out: Example 2A

34

x = 12

34

x =. 43

12

. 43

2

1

=x 23

Multiply by the reciprocal of .34

Then simplify.

34

= 12

x =


Check It Out: Example 2B

3x = 67

67

x =. 13

67

. 131

2

x = 27

3x =

3

Multiply by the reciprocal of 3.

Then simplify.



The amount of copper in brass is of the total weight.

If a sample contains 4 ounces of copper, what is the

total weight of the sample?

Additional Example 3: Physical Science Application34

15

Let w represent the total weight of the sample.

34

w = 4 15

34

w · 43

= 4 15

· 43

w = 215

· 43

7

1

w = 285

or 5 35

Write an equation.

Multiply by the reciprocal of 34

·

Write 4 15

as an improperfraction.

Then simplify.

The sample weighs 535

ounces.


The amount of copper in zinc is of the total weight. If

a sample contains 5 ounces of copper, what is the

total weight of the sample?

Check It Out: Example 314

13

Let w represent the total weight of the sample.

14

w = 5 13

14

w · 41

= 5 13

· 41

w = 163

· 41

w = 643

or 21 13

Write an equation.

Multiply by the reciprocal of 14

·

Write 5 13

as an improperfraction.

Then simplify.

The sample weighs 2113

ounces.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz

Solve. Write each answer in simplest form.

1.

2.

3.

4.

1x – 38 =

58

y + 716

= 1932

x4

= 37

34

=x 1 13

5. During the week, Marissa ate some apples from a basket. She left 20 apples. This was five-eights the number of apples she had bought earlier in the week. How many apples did she buy? 32

5 3212 7

5 7

or 1

16 9

7 9

or 1


1. Solve. Write your answer in simplest form.

x – =

A. x = C. x = or 1

B. x = D. x =


5 8

7 8

8 7

2 7

5 7

3 7

1 7



a + =

A. a = C. a = or

B. a = D. a =


23

28 3 28

18

28 1 14

5 14

13 28

9 14



3m =

A. m = C. m = or 1

B. m = D. m =


3 5

2 15

6 5

5 6

2 5

1 5



e = 1

A. e = C. e = 4

B. e = or 3 D. e = or 4


3 10

10 3

1 5

24 5

1 4

1 5

1 3

4 5


5. Harry made 18 bookmarks last week. This was nine-sixths the number of bookmarks that Ruth made. How many bookmarks did Ruth make?

A. 12 bookmarks

B. 11 bookmarks

C. 10 bookmarks

D. 9 bookmarks


3-8 solving equations containing fractions warm up warm up lesson presentation lesson presentation...

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