Section 3.6 Adding and Subtracting Fractions PRE … · Section 3.6 — Adding and Subtracting Fractions and Mixed Numbers 321 Steps in the Methodology Example 1 Example 2 Step 4

319

PRE-ACTIVITY

PREPARATION

In our U.S. measuring system, numbers are often presented as fractions—cooking and carpentry come readily to mind—so your ability to work with them is a computational skill not to be overlooked. Moreover, your further study of mathematics and other quantitative courses in a variety of fi elds will assume your competency and comfort with fractions.

If you have already built an 18¼ by 20⅝ feet deck and now wish to add a railing along three sides, how do you determine the linear feet of rail you will need? How do you account for the two 4½ feet wide entrances to the deck that must remain open? This practical application requires basic addition and subtraction of mixed numbers.

• Master the addition of fractions and mixed numbers.

• Master the subtraction of fractions and mixed numbers.

• Gain an understanding of borrowing with mixed numbers.

Adding and Subtracting Fractionsand Mixed Numbers

LLEARNINGEARNING OOBJECTIVESBJECTIVES

TTERMINOLOGYERMINOLOGY

PREVIOUSLY USED

addend mixed number

borrowing multiplier

build up numerator

common denominator proper fraction

equivalent fraction reduce

improper fraction Least Common Denominator (LCD)

minuend

Section 3.6

320 Chapter 3 — Fractions

Steps in the Methodology Example 1 Example 2

Step 1

Write the problem.

Write the problem with the correct operation sign.

Step 2

Add or subtract the numerators.

Add (or subtract) the numerators and place the sum (or difference) over the fractions’ common denominator.

Step 3

Convert to mixed number if necessary.

Convert an improper fraction answer to a mixed number.

Adding or Subtracting Proper or Improper Fractions with the Same Denominator

Example 1: Find the sum of

Example 2: Subtract

►►

►►

4

5 and

3

5.

5

8

7

8 from .

45

35

+ 78

58

−

VISUALIZE

78

58

shaded (X'd)−

7 58

28

− =

X X XX X

VISUALIZE

45

35

shaded + shaded

4 35

75

+ =

28

is a proper fraction

75

125

=

VISUALIZE

125

MMETHODOLOGIESETHODOLOGIES

The methodologies for addition and subtraction are based upon the concept introduced in the previous section— in order to add or subtract fractions, they must share a common denominator.

The fi rst methodology presents the simple process to use when the denominators are the same. It is followed by a methodology for adding or subtracting proper or improper fractions when the denominators are different.

321Section 3.6 — Adding and Subtracting Fractions and Mixed Numbers


Step 4

Reduce.

Reduce the fraction to lowest terms.

Step 5

Present the answer.

Present your answer.

Step 6

Validate your answer.

Validate your answer with the opposite operation.

Begin with your answer, and match the result to the original addend or minuend.

Note: If your answer is a mixed number or if it has a new (reduced) denominator, refer to the following Methodologies.

125

75

35

3545

=

− −

14

22

28

58

5878

× =

+ +

MMODELODEL

Add:

Steps 1 & 2

Steps 3 & 4

Step 5 Answer:

Step 6 Validate:

7

9+

4

9+

1

9

79

49

19

+ + = + + =7 4 19

129

129

139

113

= ⇒ ÷÷= 1

3 39 3

125

14

25

is reduced

2 28 2

14

÷÷=

VISUALIZE

X X XX X

¼

113

113

139

19

19

129

=

− = −

129

119

49

4979

=

− = −



Step 1

Set up the problem.

Set up the problem vertically.

Step 2

Determine the LCD.

Determine the LCD of the fractions and identify the multipliers needed to build up equivalent fractions with the LCD.

LCD = 12 by inspection

Multiplier for 3 is 4


LCD = 36 by inspection


Step 3

Build equivalent fractions.

Build equivalent fractions using the LCD and set up the problem with the equivalent fractions.

Step 4

Add or subtract the numerators.

Add (or subtract) the numerators and place the sum (or difference) over the common denominator.

Adding or Subtracting Proper or Improper Fractions with Different Denominators

Example 1: Find the sum of

Example 2: Subtract:

►►

►►

2

3 and

3

4.

5

9− 5

36

To add or subtract fractions whose denominators are not the same, you must fi rst convert them to equivalent fractions with a common denominator (the LCD, for example). This methodology includes this necessary step.

? ? ? Why do you do this?

23

+ 34

59

− 536

23

44

34

33

8129

12

× =

+ × = +

59

44

536

2036536

× =

− = −

23

44

812

34

33

9121712

× =

+ × = +

59

44

2036

536

5361536

× =

− = −



Step 5

Convert to mixed number if necessary.

Convert an improper fraction answer to a mixed number.

Step 6

Reduce.

Reduce the fraction to lowest terms.

Step 7

Present the answer.


Step 8


Validate your answer with the opposite operation.

Begin with your answer and match the result to the original addend or minuend.

Note: If your answer is a mixed number, refer to the following methodology.

1712

1512

= 1536

is proper

512

is reduced15 336 3

512

÷÷=

512

1512

1512

1512

1712

34

33

912

9128

12

= =

− × = − =−

512

33

1536

536

5362036

× =

+ =+

8 412 4

23

÷÷

= 20 436 4

59

÷÷

=

You can add or subtract fractional parts of a whole and come up with an accurate description of the result only if the parts are based upon the same number of parts in a whole—that is, the same denominator.

Visualize two small pan pizzas, each partially eaten so that one third (1/3) of a pizza remains on one pan and one fourth (1/4) remains on the other.

If you were to combine them onto one pan, how much pizza remains?

You cannot simply add the 1 and the 1 in the numerators because they represent different sized parts. And what would you use as a denominator? Only when you use their fraction equivalents can you describe the sum of these fractional parts.

1

3?+ =1

4

1

41

3

? ? ? Why do you do Step 3?


Now, instead of the one whole pizza being divided into 3 equal slices and the other pizza divided into 4 equal slices, visualize each pizza having been cut into 12 equally-sized slices so that 1/3 pizza is the same amount as 4 of 12 slices, and 1/4 pizza is the same amount as 3 of 12 slices.

Now you can reassemble/combine/add 4 equally-sized slices and 3 equally-sized slices to make 7 slices (parts)of a whole 12-slice pizza—that is, 7/12 of a whole pizza.

Similarly, you cannot subtract fractions unless they have the same denominator.

For example,

1

3

4

12=

1

4

3

12=

+ = 1

2

34 5

67

1

3+ = + =1

4

4

12

3

12

7

12

1

3− = − =1

4

4

12

3

12

1

12.

MMODELODEL

Add:

Step 1 Step 2

Steps 3 & 4 Step 5 & 6

Step 7

Step 8 Validate:

9

14+ +11

21

1

6

914112116

+

Multipliers: 42 14 342 21 242 6 7

÷ =÷ =÷ =

914

33

2742

1121

22

2242

16

77

7425642

× =

× =

+ × = +

5642

114 1442 14

113

= ÷÷

=

Answer : 113

116

77

1742

1121

22

2242

× =

− × = −

113

22

126

16

16

116

× =

− =−

=

= −

÷÷=

4942224227 342 3

914

14 2 721 3 76 2 3

2 3 7 42

= ×= ×= ×= × × =LCD


Adding Mixed Numbers


Step 1

Set up the problem.

Set up the problem. Stack the problem vertically.

For ease of calculation when adding mixed numbers, align the whole numbers and align the fractions.

Step 2

Determine the LCD.

If the denominators are the same, skip to Step 4.

If the denominators are different, determine the LCD of the fractions and identify the multipliers needed to build up equivalent fractions with the LCD.

LCD = 2×2×3×5 = 60Identify the multipliers: 60 ÷ 12 = 5 60 ÷ 15 = 4

Step 3


Build equivalent fractions using the LCD and set up the problem with the equivalent fractions.

Step 4

Add.

Add the whole numbers separately from the fractional components.

Note: Refer to the methodology for adding fractions with the same denominator.

Example 1:

Example 2:

►►

►►


8 37

12

13

15+

4 25

6

3

8+

8712

31315

+

2 12 15

2 6 15

3 3 15

5 1 5

1 1

Try It!

8712

8712

55

8

31315

31315

44

3

35605260

= × =

+ = + × = +

8712

8712

55

83560

31315

31315

44

35260

118760

= × =

+ = + × = +

MMETHODOLOGIESETHODOLOGIES

The following two methodologies address how to add and how to subtract mixed numbers.



Step 5

Convert improper fractions.

In the answer, convert an improper fractional component to a mixed number and add the whole number parts.

Step 6

Reduce.

Reduce the fractional component to lowest terms.

Step 7

Present the answer.


Step 8


Validate your answer by subtraction, using the Methodology for Subtracting Mixed Numbers.

Begin with your fi nal answer, use the original fraction and/or mixed numbers in the validation, and match the result to the original addend.


Since a mixed number is simply the addition of a whole number plus a fraction, the example problem can be

rewritten as

The Commutative Property of Addition allows you to rearrange the terms: and arrive at the same answer.

The Associative Property of Addition allows you to add as follows: and arrive at the same answer.

That is, to add the mixed numbers, you can add the whole numbers and separately add the fractions; then combine the results.

87

123

13

15+ + + .

8 37

12

13

15+ + + ,

8 37

12

13

15+( ) + +

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟ ,

11 11

122760

8760

12760

= +

=

12920

1227 360 3

12920

÷÷=

1315

60+

12920

33

122760

1227

6011

8760

344

35260

11× = = =

− × = − = − =−35260

35260

83560

= =835

608

712

7

12

Note: You will learn subtraction of mixed numbers in the next methodology (see page 328).


MMODELSODELS

Add:

Step 1 Step 2

Steps 3 & 4

Steps 5 & 6

Step 7

Step 8 Validate:

45

6

3

41

6

7+ +

2 6 4 7

2 3 2 7

3 3 1 7

7 1 1 7

1 1 1

LCD = 2 × 2 × 3 × 7 =84

Multipliers:

84 ÷ 6 = 14

84 ÷ 4 = 21

84 ÷ 7 = 12

45634

167

+

Model 1

520584

5 23784

73784

= + = 372 2 3 7• • •

reduced

Answer : 73784

456

1414

47084

34

2121

6384

167

1212

17284

520584

× =

× =

+ × = +

73784

737

846

167

1212

6 84

12184

= =

− × =

+

−− = −

÷÷=

17284

17284

549 784 7

5712

5712

57

124

1912

34

33

912

912

4

4 12

= =

− × = − = −

+

5

6

10

124

56

=


Model 2

Add:

Step 1 Step 2 LCD is 36, by inspection

Step 5

Step 6 23 is prime and is not a factor of 36.

Step 7

Step 8 Validate:

128

913 15

3

4+ +

1289

13

1534

+

405936

40 12336

412336

= + =

Answer : 412336

Steps 3 & 4

2336

is fully reduced.

412336

4123

3640

1534

99

152736

15

40 36

5936

= =

− × = − = −

+

22736

253236

2589

=

2589

13

1289

−

1289

44

123236

13 13

1534

99

152736

405936

× =

=

+ × = +

Note: Keep the whole number as it is.


Step 1

Set up the problem.


For ease of calculation when subtracting mixed numbers, align the whole numbers and align the fractions.

Example 1:

Example 2:

Subtracting Mixed Numbers

►►

►►

68

213

2

3−

31

81

2

3− Try It!

6821

323

−


continued on the next page


Step 2

Determine the LCD.

If the denominators are the same, skip to Step 4.

If the denominators are different, determine the LCD of the fractions and identify the multipliers needed to build up equivalent fractions with the LCD.

21 is divisible by 3.

21 is the LCD.

21 ÷ 3 = 7

Step 3


Build equivalent fractions using the LCD (refer to Section 3.5) and set up the problem using the equivalent fractions.

Step 4

Borrow if necessary.

Determine if borrowing from the whole number part of the top number is necessary. Borrowing is necessary when the numerator of the fi rst fraction is less than the numerator of the second fraction.

Borrowing with Fractions

To borrow using fractions:

• Reduce the ones digit in the whole number by one (1).

• Rewrite the borrowed 1 as a fraction, using the common denominator.

8 < 14Borrowing is necessary.

OR

Use this notation:

Step 5

Subtract.

Subtract the whole numbers separately from the fractional numbers.

Note: Refer to the Methodology for Subtracting Fractions with the Same Denominator.


5 21

68

215

2921

+=

5 21

68

215

2921

31421

31421

21521

+=

− = −

6821

5 1821

521

821

52921

21

= + +

= + + =

Special Case:

Subtracting a mixed number from a whole number (see page 332, Model 1)

6821

6821

6821

323

323

77

31421

= =

− = − × = −



The borrowing process for a mixed number subtraction problem focuses on the common denominator of the fractions.

A way to understand this borrowing process might be to think of it in terms of a familiar example. Imagine yourself as a baker selling whole sheet cakes and individual servings that you form by slicing a whole cake into 21 equal portions (think denominator).

For Example 1, visualize the cakes you have on hand today:

6 whole cakes and 8 individual servings

6 whole cakes and of another, or cakes8

216

8

21


Step 6

Reduce.


Step 7

Present the answer.


Step 8


Validate your answer by addition, using the Methodology for Adding Fractions and Mixed Numbers.

Begin with your fi nal answer, use the original fractions and/or mixed numbers in the validation, and match the result to the original fi rst number.

257

257

33

21521

323

323

77

31421

52921

= × =

+ = + × = +

52921

5 1821

6821

= + =

21521

23 5

3 72

57

1

1= •

•=

257


Although you can easily sell 3 whole cakes from the 6, you cannot serve 14 pieces from the 8 cut pieces available. However, the solution is to slice one of the 6 whole cakes into 21 pieces.

Why 21? —to match the already determined size of your portions (think LCD determined in Step 2). This borrowing results in a rearrangement of the mixed number, giving you 5 whole cakes + 1 whole cake cut into 21 pieces + the original 8 pieces on hand.

That is, 68

215 1

8

215

21

21

8

215

29

21= + + = + + =

XX X

X X

X X

X X

This enables you to take 14 pieces from the 29 pieces and 3 whole cakes from the 5 still-uncut whole cakes

(X’d out below), leaving you with cakes, or 2 whole cakes and of another (shaded below).215

21

15

21

X X X

X X X

X X


MMODELSODELS

Model 1

Subtract: 13 53

8−

Step 1

Steps 2 & 3 There is only one fraction. It remains the same. Skip to Step 4.

Step 4

Steps 5 & 6

Step 7

Step 8 Validate:

When subtracting a mixed number from a whole number, there is no fractional component to subtract from. Borrowing is necessary. Use the denominator of the bottom fraction as the LCD.

13 1288

= + or 1288

13

538

−

13 1288

538

538

758

=

− = −

reduced

Answer : 758

758

538

1288

12 1 13

+

= + =

Subtracting a Mixed Number from a Whole Number

Model 2

Subtract: 184

512−

Step 1

Step 2 There is only one fraction, . Skip to Step 4.

Step 4 Borrowing is not necessary in

this case because is the

top fraction, from which no

fraction is being subtracted.

Step 5

Step 6 is reduced.

Step 7

Step 8 Validate:

1845

12

−

1845

12

645

−

45

Answer : 645

45

45

645

+12

1845

Special Case:


Model 3

Step 1 Step 2 9 = 3 × 3

6 = 2 × 3

LCD = 2 × 3 × 3 = 18

Steps 3, 4 & 5

or use the notation:

Step 6

Step 7

Step 8 Validate:

Subtract from 35

67

4

9.

749

356

−

74 29 2

78

186

1818

818

62618

35 36 3

31518

••= = + + =

− ••= − =

−31518

31118

6 187

818

31518

+

−

=

= −

62618

31518

31118

1118

112 3 3

=• •

reduced

Answer : 31118

31118

31118

3

=

+ 556

33

31518

62618

6 18

187

8

187

49

4

9

× =

= + = =



Step 1

Set up the problem.


Step 2

Write as improper fractions.

Change the mixed numbers to improper fractions.

Step 3

Determine the LCD.

Determine the LCD. LCD = 24,

by inspection

Step 4

Build up fractions.

Using the LCD, build equivalent fractions. Set up the problem with the equivalent fractions.

Step 5

Add or subtract numerators.

Add or subtract the numerators as indicated in the problem.

Example 1:

Example 2:

Adding and Subtracting Mixed Numbers by Conversion to Improper Fractions

optional, alternate methodology

►►

►► Try It!

31

81

2

3−

45

81

11

12−

318

123

−

318

258

123

53

=

− = −

258

25 38 3

7524

53

5 83 8

4024

= ••=

− = − ••= −

MMETHODOLOGYETHODOLOGY

258

25 38 3

7524

53

5 83 8

40243524

= ••=

− = − ••= −

The following is an alternate methodology for adding or subtracting mixed numbers. It avoids the process of borrowing by fi rst converting the mixed numbers to improper fractions. However, for many problems, the number of calculations combined with the size of the numbers becomes cumbersome and prone to computational errors. If you do decide to use this methodology, keep in mind that you must present the fi nal answer as a mixed number, not as an improper fraction.



Step 6

Convert to mixed number.

Convert the answer to a mixed number.

Step 7

Reduce.


11 is prime, no common factors with 24.

is reduced.

Step 8

Present the answer.


Step 9


Validate your fi nal answer with the opposite operation. Begin with your answer, use the original fractions or mixed numbers and match the result to the original term.

11124

11124

3524

3524

123

53

88

4024

7524

7524

33

243

18

1

8

= =

+ = + × = +

= =

1124

MMODELODEL

Model of Alternate Methodolgy

Steps 1 & 2

Add: 128

9+ +13 15

3

4

1289

1169

13131

1534

634

=

+ =

+ = +

Step 3 LCD is 36, by inspection

3524

11124

=


Steps 4 & 5

Step 6 )36 1499144

593623

4141

2336

−

−

Answer : 412336

Step 8

Step 7 23 is prime and not a factor of 36.

is reduced.2336

Step 9 Validate:

93236

93236

131

3636

4683

=

− × = −

66

46436

1232

3612

89

8

9= =

412336

149936

149936

1534

634

99

5673693236

= =

− = − × = −

116

4

464

×36

13

108

360

468

×

63

9

567

×464

468

567

1499

+

36

41

36

1440

1476

23

1499

×

+

63

9

567

×

1499

567

932

−

36

13

108

360

468

× )36 464

36

104

72

32

12

−

−

1169

44

46436

131

3636

46836

634

99

56736

149936

× =

× =

+ × = +


As was the case with whole numbers and decimals, estimating sums and differences of fractions and mixed numbers requires mental math skills.

It is easiest to estimate by rounding the mixed numbers to the nearest whole number, based upon how the fractional part of the mixed number compares to ½. Recall that a fraction is equal to ½ when its numerator is half its denominator.

• If the fraction is < ½, round the mixed number down to the whole number part.• If the fraction is > ½, round up to the next higher whole number.• If the fraction = ½, retain the ½.

Occasionally you might get a better estimate if you can tell if the fraction is “very close” to ½, in which case you might round to the ½ (see the fourth example below).

Example: Example:

Estimate: Estimate:

Actual answer: Actual answer:

Example: Example:

Estimate: Estimate #1: 5 – 1 = 4

Estimate #2:

Actual answer:

How Estimation Can Help

THINK

235

8

2

3 15−

As these examples remind you, estimation is not meant to be precise. However, it will give you a number against which you can determine if your answer is reasonable.

Go back and estimate the answers to the fi rst and second Examples of the Methodologies for Adding and for Subtracting Fractions and Mixed Numbers. Was each answer reasonable as compared to its estimate?

THINK3

4>

1

2

1

3<

1

2

1

2=

1

2

83

42

1

3

1

2 + +

5

8>

1

2

2

3>

1

2

9 21

2 11

1

2+ + = 24 16 8− =

1131

48, a bit larger than 11

1

27

23

24, close to 8

387

92

13

15 + 4

18

35

1

10 1−

39 42 + 3 =

4129

45,

a bit closer to 42 than to 413

29

70, closer to 3

1

2 than to 4

Actual answer: 41

2

1

2 − =1 3


AADDRESSING DDRESSING CCOMMON OMMON EERRORSRRORS

Issue Incorrect Process Resolution Correct

Process Validation

Incorrectly identifying the number of parts in a whole when borrowing from the whole number for subtraction

When borrowing, the borrowed “1” must be in fraction form, using the denominator of the given fractions.

Not reducing the fi nal answer to lowest terms

Do a prime factorization of your fi nal answer to assure that there are no remaining common factors to cancel.

Not adjusting the numerator to balance the change in the denominator when writing equivalent fractions

Use the Methodology for Building Equivalent Fractions (see Section 3.5). Apply the Identity Property of Multiplication.

523

546

546

256

256

256

296

4 1

= =

− = − = −

296

336

312

= =

546

466

46

4106

256

256

256

256

= + + =

− = − = −

256

256

4106

4 146

54

65

23

2

3

+

= +

= =

35

8340

58

5540

840

15

× =

+ × = +

=

35

88

2440

58

55

2540

4940

1940

× =

+ × = +

=

1940

19

404940

58

55

2540

2540

2440

0 40= =

− × = − = −

+

2440

24

40

35

3

5= =

814

33

83

12

5712

5712

131012

× =

+ = +

814

33

83

12

5712

5712

131012

× =

+ = +

Answer: 131012

131012

132 5

2 2 2

1356

1

1= •

• •

=

1356

22

131012

5712

5712

83

12

× =

− = −

83

128

14

=

continues on the next page

=6

54 =

=56

=

sw 3er:

5 +

45

=88

4

×8

+


PPREPARATION REPARATION IINVENTORYNVENTORY

Before proceeding, you should have an understanding of each of the following:

the terminology and notation associated with adding and subtracting fractions and mixed numbers

why you need a common denominator to add or subtract fractions and mixed numbers

what it means to borrow from the whole number in order to subtract fractional parts

how to validate the answer to an addition or subtraction problem when the terms are fractions or mixed numbers

Issue Incorrect Process Resolution Correct

Process Validation

Forgetting to include the whole number parts of mixed numbers

For mixed number addition and subtraction, vertically align the whole numbers and align the fractions.

When you need to rewrite the fractional parts of mixed numbers, always bring along the whole number parts as well, before adding or subtracting.

Not borrowing when subtracting from a whole number

When you subtract a mixed number from a whole number, you must borrow from the whole number in order to subtract the fractional part of the mixed number.

Use the denominator of the bottom fraction as the LCD when you borrow.

234

33

912

523

44

812

1712

1712

1512

× =

+ × = +

=

234

33

29

12

523

44

58

12

71712

71712

7 1512

8512

× =

+ × = +

= +

=

8512

85

127

1712

523

44

58

125

812

29

12

7 12

= =

− × = − = −

+

29

122

34

3

4 =

42

4×

4

× =

=

34 3

4

×

=

7

425

325

−

7

45

7 655

425

425

235

=

− = −

235

425

655

6 1

7

+

= +

=

340

ACTIVITY

PPERFORMANCE ERFORMANCE CCRITERIARITERIA

• Adding any combination of fractions and mixed numbers correctly – fi nal answer in mixed number, fully reduced form – validation of the fi nal answer

• Subtracting any combination of fractions and mixed numbers correctly – fi nal answer in mixed number, fully reduced form – validation of the fi nal answer

CCRITICAL RITICAL TTHINKING HINKING QQUESTIONSUESTIONS

1. What is the best way to set up the addition or subtraction of mixed numbers?

2. Why do you need a common denominator to add or subtract fractions?

3. Why is it to your advantage to use the Least Common Denominator when adding or subtracting fractions?

4. Where is the Identity Property of Multiplication used in the addition and subtraction of fractions?

Adding and Subtracting Fractionsand Mixed Numbers

Section 3.6


5. What is the meaning of borrowing within mixed number subtraction?

6. What are the advantages and disadvantages of the alternate Methodology for Subtracting Mixed Numbers?

7. Why is it important to use terms from the original problem when you validate your presented answer?

TTIPS FOR IPS FOR SSUCCESSUCCESS

• For ease of computation and for clarity when presenting an answer, use a horizontal fraction bar rather than a slash.

• If alignment is a problem, use a vertical line between the whole numbers and the fractional parts of mixed numbers as shown in the Models.

• The LCD is the easiest common denominator to use.

• Use effective notation for borrowing.

• Always validate your fi nal answer using the original fraction or mixed number terms. Otherwise you may not detect the interim errors that may have been made in building up or reducing.

2

3 not 2/3

⎛⎝⎜⎜⎜

⎞⎠⎟⎟⎟


DDEMONSTRATE EMONSTRATE YYOUR OUR UUNDERSTANDINGNDERSTANDING

Problem Worked Solution Validate

1)

2)

3)

512

716

34

+ +

2856

10712

−

6 249

−



4)

5)

6)

329

2 145

+ +

5712

2−

1115

2710

734

+ +



7)

8)

913

567

−

Subtract

from 1238

1517

TEAM EXERCISETEAM EXERCISE

One third (1/3) of the monthly income for my family is used to pay the rent, one twelfth (1/12) of it is used to pay the utilities, one fourth (1/4) of it is used to pay for food, and one eighth (1/8) of the monthly income is used to make the car payment. What part of my family’s monthly income is left for other things?


IDENTIFY AND CORRECT THE ERRORSIDENTIFY AND CORRECT THE ERRORS

In the second column, identify the error(s) you fi nd in each of the following worked solutions. If the answer appears to be correct, validate it in the second column and label it “Correct.” If the worked solution is incorrect, solve the problem correctly in the third column and validate your answer in the last column.

Worked SolutionWhat is Wrong Here?

Identify Errors or Validate Correct Process Validation

1) Just broght down the 1/3.

Did not borrow from the whole number 6 to subtract the 1/3.

2)

3)

6 413

−

314

158

−

513

278

−

6 5 33

4 13

4 13

123

=

− = −

Answer: 123

123

4 13

5 33

5 1

6

+

= +

=


Worked SolutionWhat is Wrong Here?

Identify Errors or Validate Correct Process Validation

4)

5)

735

1710

+

214

138

2712

+ +


ADDITIONAL EXERCISESADDITIONAL EXERCISES

Solve each of the following and validate your answers.

1.

2.

3.

4.

5.

6.

7.

8. Subtract

2

3

5

6

7

9+ +

52

52

1

4−

145

129−

151

37

11

1540

7

9+ +

161

511

3

4−

5

211

3

144

5

18+ +

25 55

8−

411

15

2

5 from 16

Documents

Section 3.6 Adding and Subtracting Fractions PRE … · Section 3.6 — Adding and Subtracting Fractions and Mixed Numbers 321 Steps in the Methodology Example 1 Example 2 Step 4