Unit 2

Common Fractions

2

FRACTION A fraction is a value that shows the number of

equal parts taken of a whole quantity or unitFractions can be expressed in lowest terms

by dividing both the numerator and denominator by their greatest common factor

To reduce to lowest terms, divide both the numerator and denominator by 5

Ans5

3

525

515

25

15

3

MIXED NUMBERS AS FRACTIONS

A mixed number is a whole number plus a fraction

To express a mixed number as an improper fraction:Find number of fractional parts contained

in the whole number Add the fractional part to the whole number

equivalent

4

MIXED NUMBERS AS FRACTIONS

Find the number of fractional parts contained in the whole number

Add the fractional part

:fractionaas54

3Express

5

15

5

5

1

3

Ans5

1954

515

5

FRACTIONS AS MIXED NUMBERS

To convert fractions into mixed numbers, divide and place the remainder over the denominator

numbermixedaas3275

Express

275326411

Ans3211

2

6

ADDITION OF FRACTIONS

Requires a common denominator Least common denominator is smallest number

that all denominators divide into evenly

First, determine the LCD:

6 = 2 × 3; 3 = 1 × 3; 15 = 3 × 5

LCD = 2 × 3 × 5 = 30

154

31

65

:Add

7

ADDITION OF FRACTIONS

Next, convert every fraction to 30ths:

30

10

10

10

3

1

30

25

5

5

6

5

30

8

2

2

15

4

8

ADDITION OF FRACTIONS

Finally, add the numerators of the fractions and convert to a mixed number:

.30

131

30

43

30

8

30

10

30

25Ans

9

SUBTRACTION OF FRACTIONS

Subtraction of fractions requires a common denominator.

First, determine the prime factors of each denominator: 16 = 2 × 2 × 2 × 2

8 = 2 × 2 × 2

8

3

16

15:Subtract

10

SUBTRACTION OF FRACTIONS

Then determine the LCD:

2 × 2 × 2 × 2 = 16

Next, convert 3/8 to 16ths:

166

22

83

11

SUBTRACTION OF FRACTIONS

Finally, subtract the numerators of the fractions:

Ans169

166

1615

12

LOWEST COMMON DENOMINATORS

Use prime factoring when LCD is difficultFactor each denominator into prime factorsList each prime factor the most times it

appears in any one denominatorMultiply all the prime factors listed

13

LOWEST COMMON DENOMINATORS (Cont)

Find the lowest common denominator:

Prime factor each denominator

103

127

98

339

32212

5210

14

LOWEST COMMON DENOMINATORS (Cont)

List each prime factor the most times it appears in any one denominator

3 × 3 × 2 × 5 × 5

Multiply the factors

180 Ans

15

MULTIPLICATION OF FRACTIONS

Multiplication and division of fractions do not require a common denominator

To multiply simple fractions, multiply the numerators and multiply the denominators

Mixed numbers must be changed to improper fractions before multiplying

16

7

6

5

2Multiply

Ans35

12

75

62

7

6

5

2

MULTIPLICATION OF FRACTIONS

17

MULTIPLICATION OF FRACTIONS

3

5to

3

21changeFirst,

Ans214

12125

7355

75

35

7

5

3

21:Multiply

18

DIVISION OF FRACTIONS

To divide fractions, invert the divisor, change to the inverse operation, and multiply.

5

4

9

2:Divide

Ans185

3610

4952

45

92

19

57

to52

1

Ans51

4521

13

57

31

57

DIVISION OF FRACTIONS

First, change

Next, divide

31

52

1Divide :

20

ORDER OF OPERATIONS

As with any arithmetic expression, the order of operations must be followed. The operations are:

ParenthesesExponentsMultiplication and division from left to rightAddition and subtraction from left to right

21

Ans4039

23

2013

32

2013

ORDER OF OPERATIONS

First, addition in ( )

Next, division

2013

208

205

52

41

32

52

41

Evaluate

:

22

PRACTICE PROBLEMS

1. Reduce each of the following:

a. b. c.

2. Express these mixed numbers as improper fractions:

a. b. c.

3. Express these improper fractions as mixed numbers:

a. b. c.

2718

6054

624105

32

254

341

12

47

373

35140

23

PRACTICE PROBLEMS (cont.)

4. Perform the indicated operations:

65

131

354

6c.

21

43

31

b.

52

31

a.

65

54

e.

97

413d.

43

287

1f.

24

PRACTICE PROBLEMS (cont)

54

75

32

1h.

3530

152

g.

41

21

41

3217

j.

51

21

1032

i.

4. Perform the indicated operations:

25

Practice Problems

5. Calculate dimensions A-E using the template

26

Solutions

1. Reducea. A

b. B

c. C

2. Mixed to improper

a. A

b. B

c. C

3

2

10

9

208

35

3

8

5

19

4

49

3. Improper to mixed

a. A

b. B

c. 4

4

31

3

124

27

Solutions

4. operationsa. A

b. B

c. C

d. A

e. B

f. C

15

11

12

7

10

38

3

2

9

28

32

55

g. A

h. B

i. C

j. D

45

7

84

411

15

813

64

9

28

Solutions

5. templateA. A

B. B

C. C

32

58

32

73

64

94

8

72

16

11

D. A

E. B