Holt CA Course 1 4-6 Solving Equations Containing Fractions Warm Up Warm Up California Standards...

Holt CA Course 1

4-6 Solving Equations Containing Fractions

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Holt CA Course 1


Warm Up in Spiral.Solve.

1. x – 16 = 8

2. 7a = 35

3.

4. y + 21 = 31

x = 24

a = 5

x = 132x12

= 11

y = 10

Holt CA Course 1


AF1.1 Write and solve one-step linear equations in one variable.Also covered: NS2.1, NS2.2, NS2.4

California Standards

Holt CA Course 1


The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to get the variable by itself on one side of the equation.

Holt CA Course 1


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

x = 87

=1 17

Simplify.

37

Since is subtracted from x, 37

add to both sides.

Think: What is happening to x. How do I undo that?

Holt CA Course 1



Additional Example 1B: Solving Equations by Adding or Subtracting

512

+ t =38

38

+ t = 512

Find a common denominator.

Subtract.

38

+ t – =5

12–

38

38

t = 1024

– 924

t = 124

Since is added to t, 38

38

subtract from both sides.

Holt CA Course 1



Additional Example 1C: Solving Equations by Adding or Subtracting

49

+ r = 12

49

+ r = 12

49

+ r – 49

= 12

– 49


Subtract.r = 118

–r = 918

818

Since is added to r, 49

49subtract from both sides.

Holt CA Course 1


Check.Additional Example 1C Continued

49

+ r = 12

=918

918


Add.

You can check that a value is a solution to an equation by substituting the value for the variable. Substitute and solve. Is it correct?

Helpful Hint

Substitute for r.1

1849

+ 1 18

12

=?

818

+ 118

918

=?

Holt CA Course 1



Check It Out! Example 1A

x – 38

= 78

x – 38

= 78

x – 38

+ 38

= 78

+ 38

x = 10 8

= 1 14

Simplify.

Since is subtracted from x, add to both sides.

38

38

Holt CA Course 1



Check It Out! Example 1B

14

+ y = 38

14

+ y = 38

14

38

14

+ y– = – 14

38

y = – 28

y = 18


Subtract.

Since is added to y, subtract from both sides.

14

14

Holt CA Course 1


Check.

Check It Out! Example 1B Continued

14

+ y = 38

=38

38


Add.

Substitute for y.18

14

+ 1 8

38

=?

28

+ 18

38

=?

Holt CA Course 1



Check It Out! Example 1C

314

+ t = 27

314

+ t = 27


Subtract.

314

+ t – = 27

–3

143

14

t = – 314

414

t = 114

Since is added to t, 3

14

subtract from both sides.3

14

Holt CA Course 1



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 .

Holt CA Course 1


Additional Example 2B: Solving Equations by Multiplying

4y = 8989

4y = 14

89

141

2

y = 29

4y = Multiply by the reciprocal of 4.

Then simplify.


Holt CA Course 1



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 =

Holt CA Course 1


Check It Out! Example 2B

3y = 6767

y = 13

67

131

2

y = 27

3y =

3

Multiply by the reciprocal of 3.

Then simplify.


Holt CA Course 1

4-6 Solving Equations Containing FractionsAdditional Example 3: Physical Science Application

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?

34

15

Let w represent the total weight of the sample.34

w = 4 15

34

w 43

= 4 15 4

3

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.

Holt CA Course 1


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.

Multiply.

The sample weighs 2113

ounces.

Holt CA Course 1

4-6 Solving Equations Containing FractionsLesson 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. Over the course of a week, Marissa ate some apples from a basket on the table. She left 20 apples in the basket. This was five-eighths the number of apples her mother had picked earlier in the week. How many apples did her mother pick? 32

5 3212 7

5 7

or 1

16 9

7 9

or 1

Holt CA Course 1 4-6 Solving Equations Containing Fractions Warm Up Warm Up California Standards...

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