5-10 Solving Fraction Equations: Addition and Subtraction

Course 1

Warm Up

Lesson Presentation

Problem of the Day

Warm UpSolve.

1. x – 15 = 9

2. x + 21 = 34

3. 17 = x – 11

4. 22 = x – 34

x = 24

x = 13

x = 28

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

x = 56

Problem of the Day

If a newborn baby weighs two pounds plus three-fourths its own weight, how much does it weigh?

8 pounds

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Learn to solve equations by adding and subtracting fractions.

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Additional Example 1A: Solving Equations by Adding and Subtracting

Solve the equation. Write the solution in simplest form.

3

5__

x + 5 = 143

5__

3

5__ – 5 – 5

3

5__

______ ______

x = 13 – 53

5__5

5__

x = 82

5__

Subtract 5 from both sides to undo addition.

3

5__

Rename 14 as 13 . 5

5__

Subtract.

A. x + 5 = 14

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Additional Example 1B: Solving Equations by Adding and Subtracting

Solve the equation. Write the solution in simplest form.

2

9__

3 = x – 42

9__

1

3__ + 4 + 4

1

3__

______ ________

3 + 4 = x3

9__2

9__

7 = x5

9__

Add 4 to both sides to undo the

subtraction.

1

3__

Find a common denominator.

Add.

1

3__

1

3__

B. 3 = x – 4

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Additional Example 1C: Solving Equations by Adding and Subtracting

Solve the equation. Write the solution in simplest form.

1

6__

6 = m +1

6__

7

12__ – –

7

12__

______ ______

6 – = m7

12__2

12__

5 = m7

12__

Subtract from both sides to undo the

addition.

7

12__

Find a common denominator.

Subtract.

7

12__

7

12__

5 – = m7

12__14

12__

Rename 6 as 5 + . 2

12__ 12

12__ 2

12__

C. 6 = m +

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Additional Example 1D: Solving Equations by Adding and Subtracting

Solve the equation. Write the solution in simplest form.

4

5__

w – = 34

5__

4

5__ + + 4

5__

_____ _____

w = 3 +4

5__3

10__

w = 3 +3

10__

Add to both sides to undo subtraction.

4

5__

Find a common denominator.

Add.

3

10__

3

10__

8

10__

w = 3

w = 4

11

10__

1

10__

3 = 3 + 1 . 11

10__ 1

10__

D. w – = 3

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Try This: Example 1ASolve the equation. Write the solution in simplest form.

5

8__

x + 3 = 125

8__

5

8__ – 3 – 3

5

8__

______ ______

x = 11 – 35

8__8

8__

x = 83

8__

Subtract 3 from both sides to undo addition.

5

8__

Rename 12 as 11 . 8

8__

Subtract.

A. x + 3 = 12

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Try This: Example 1BSolve the equation. Write the solution in simplest form.

3

8__

2 = x – 33

8__

1

4__ + 3 + 3

1

4__

______ ______

2 + 3 = x2

8__3

8__

5 = x5

8__

Add 3 to both sides to undo the

subtraction.

1

4__

Find a common denominator.

Add.

1

4__

1

4__

B. 2 = x – 3

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Try This: Example 1CSolve the equation. Write the solution in simplest form.

2

5__

5 = m +2

5__

7

10__ – –

7

10__

______ ______

5 – = m7

10__4

10__

4 = m7

10__

Subtract from both sides to undo the

addition.

7

10__

Find a common denominator.

Subtract.

7

10__

7

10__

4 - = m7

10__14

10__

Rename 5 as 4 + . 4

10__ 10

10__ 4

10__

C. 5 = m +

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Try This: Example 1DSolve the equation. Write the solution in simplest form.

1

3__

w – = 51

3__

1

3__ + +

1

3__

_____ _____

w = 5 +1

3__5

6__

w = 5 +5

6__

Add to both sides to undo subtraction. 1

3__

Find a common denominator.

Add.

5

6__

5

6__

2

6__

w = 5

w = 6

7

6__

1

6__

5 = 5 + 1 . 7

6__ 1

6__

D. w – = 5

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Additional Example 2: Application1

4__

1

2__

d – 17 = 851

2__

1

2__ + 17 + 17

1

2__

________ ________

1

4__

d = 1023

4__

Let d represent the weight of Ian’s dog.

Add 17 to both sides to undo the

subtraction.

1

2__

Linda’s dog weighs 85 pounds. If Linda’s dog

weighs 17 pounds less than Ian’s dog, how

much does Ian’s dog weigh?

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Additional Example 2 Continued

Check

d – 17 = 85 1

2__ 1

4__

3

4__102 – 17 = 85

1

2__ 1

4__?

3

4__102 – 17 = 85

2

4__ 1

4__?

85 = 85 ? 1

4__1

4__

Substitute 102 for d. 3

4__

Find a common denominator.

102 is the solution. 3

4__

Ian’s dog weighs 102 pounds.3

4__

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Try This: Example 22

3__

1

6__

c – 4 = 131

6__

1

6__ + 4 + 4

1

6__

_______ ________

2

3__

c = 175

6__

Let c represent the weight of Vicki’s cat.

Add 4 to both sides to undo the

subtraction.

1

6__

Jimmy’s cat weighs 13 pounds. If Jimmy’s cat weighs

4 pounds less than Vicki’s cat, how much does Vicki’s

cat weigh?

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Try This: Example 2

Check

c – 4 = 13 1

6__ 2

3__

5

6__ 17 – 4 = 13

1

6__ 2

3__?

5

6__ 17 – 4 = 13

1

6__ 4

6__?

13 = 13 ? 4

6__4

6__

Substitute 17 for c. 5

6__

Find a common denominator.

17 is the solution. 5

6__

Vicki’s cat weighs 17 pounds.5

6__

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction

Solve each equation. Write the solution in simplest form.

1. x – 3 = 2 2. x + 6 = 11

3. 1 = x – 2 4. 5 = x –

5. Marco needs to work 40 hours per week. He has worked

31 hours so far this week. How many hours does he need

to work on Friday to meet his 40-hour requirement?

Lesson Quiz

34__ 5

12__ x = 6

16__ 5

8__

710__ 1

2__3

4__

58__

x = 438__

x = 412__ x = 6

14__

8 hours38__

45__

Course 1

5-10 Solving Fraction Equations: Addition and Subtraction