4.1 – Fractions and Mixed Numbers Fractions Defn: Numbers that show the number of parts existing...

4.1 – Fractions and Mixed NumbersFractions

Defn: Numbers that show the number of parts existing compared to the number of parts in a whole.

Numerator (a): the top number of a fraction that describes the number of parts existing.

Denominator (b): the bottom number of the fraction that describes the number of parts that make a whole.

b

a

4.1 – Fractions and Mixed NumbersWrite a fraction to represent the shaded portion of each figure.

5

2

8

5

12

7

4.1 – Fractions and Mixed NumbersWrite a fraction to represent the shaded portion of each figure.

10

7

5

3

6

5

4.1 – Fractions and Mixed NumbersDraw and shade each fraction.

7

3

4.1 – Fractions and Mixed NumbersProper Fractions

Defn: A fraction whose numerator is smaller than its denominator.

Defn: A fraction whose numerator is larger than its denominator.

Defn: A number which is made up of an integer and a fraction.

Improper Fractions

Mixed Numbers

4.1 – Fractions and Mixed Numbers

Classify each of the following fractions:

29

237

15

85

62

33

47

9

54

61

277

proper

proper

improper

improper

mixed number

mixed number


Converting Mixed Numbers to Improper Fractions1. Multiply the denominator by the integer.

2. Add the numerator to the product of the denominator and the integer.3. Write the sum as the numerator over the original denominator.

7

257 7

25

7

2357

37

3

263 3

26

3

2183

20


Converting Mixed Numbers to Improper Fractions

10

71010 10

710

10

7100 10

107

12

11812 12

118

12

1196 12

107


Converting Improper Fractions to Mixed Numbers1. Divide the numerator by the denominator.

2. The quotient is the integer of the mixed number.

3. The remainder is the numerator over the original denominator.

955

9

54

1

5

4 1


Converting Improper Fractions to Mixed Numbers

2399

23

185

2

9

5 2

621313

62

5210

4

13

10 4

4.2 – Factors and Simplest FormDivisibility Tests

1. A whole number is divisible by 2 if the number is even.

2. A whole number is divisible by 3 if the sum of the digits is divisible by 3.

3. A whole number is divisible by 4 if the last 2 digits are divisible by 4.

236

354

9126

968 140

621 (is divisible by 3)

(36 is divisible by 4) 528,10 (28 is divisible by 4)

1824831 13842 (is divisible by 3)

4.2 – Factors and Simplest FormDivisibility Tests

4. A whole number is divisible by 5 if the number ends in a 0 or a 5.

5. A whole number is divisible by 6 if it is divisible by both 2 and 3.

6. A whole number is divisible by 9 if the sum of the digits is divisible by 9.

936

345

9126

1265 140

621 (is divisible by 2 and 3)

18 (is divisible by 9)

2124834 43842 (is divisible by 2 and 3)

639

4.2 – Factors and Simplest Form

A Number as a Product of Prime Numbers

24

12

3

2

62

3222 323

2

Factor Trees24

8

2

3

42

3222 323

2

4.2 – Factors and Simplest Form

A Number as a Product of Prime Numbers

72

36

9

2

182

33222 23 32

2

Factor Trees210

105

7

2

215

7532

3

3 3

4.2 – Factors and Simplest FormSimplest Form

30

152

53

45

30533

532

Defn: A fraction is in simplest form when the numerator and denominator have no other common factors other than 1.

45

95

33

3

2


49

77

142

112

4972222

77

Write in Simplest Form.

112

562

282

16

7

2 7


20

64

16

20

64


5

16

5

common factor is 4


2

3

56

7

a

aa

2

3

56

7

a

a


8

a

8

common factor is 7a2

4.2 – Fractions and Simplest FormEquivalent Fractions – Two Methods

27

21

9

7

7

99

7

9

7

?27

21

9

7equivalentandAre

1. Simplify each fraction. 2. Cross Multiply.

27

21

9

7

189189

277219

Fractions are equivalent.


85

34

15

6

5

2

5

2

175

172

53

32

?85

34

15

6equivalentandAre


85

34

15

6

510510

8563415

Fractions are equivalent.


18

5

36

10

39

12

13

4

3322

52

133

322

?36

10

39

12equivalentandAre


36

10

39

12

390432

10393612

Fractions are not equivalent.

4.3 – Multiplying and Dividing FractionsMultiplying Fractions

1. Multiply the numerators.

2. Multiply the denominators.

3. The product of the numerators remains as the numerator as the product of the denominators remains as the denominator.

117

53

11

5

7

3

77

15

93

11

9

1

3

1

27

1


877

76

8

7

77

6

3

411

13

827

34

8

3

27

4

29

11

18

1

4

1

1144

3

1

2

1

9


1611

334

16

33

11

4

1

41

31

23

32

y

2

3

3

2 y

11

11

y y

4

3

14

3

1

1

1

1


22

3

ab

ba

22

3

a

b

b

a

a

1

1

b

a

4

3

4

3

4

3

3

4

3

3

3

4

364

27

1

1

bb

a


16106

2531

16

25

10

3

6

1

1

1622

511

2

5

264

5

4.3 – Multiplying and Dividing FractionsDividing Fractions

1. Write the reciprocal of the second fraction (the divisor).

2. Change the division operator to multiplication.

3. Work the problem as a multiplication problem.

1

2

9

4

2

1

9

4

9

8

2

5

7

8

5

2

7

8

17

54

4

1

7

20


2

9

4

10

9

2

4

10

4

45

35

1

4

3

y

y35

4

3y

y 254

113

y

1

2y

220

3

y

14

95

5

1


7

15

14

9

3

2

15

7

14

9

3

2

49

45

9

2

4

3

2

9

4

3

32

11

1

3

6

1

771

1531

1

7

3

1

.2

9

4

3, yandxifyxexpressiontheEvaluate

1

2


7

15

14

9

3

2

15

7

14

9

3

2

49

45

4

9

8

9

1

2

4

9

8

92

4

9

41

91

1

4

4

9

4

9

771

1531

1

7

3

1

?4

92

8

9 xequationtheofsolutionaIs YES


1

60

6

160

6

1

11

101

10

1

10

606

1of

Hershey Park is located in Pennsylvania. Of its sixty rides, one-sixth of them are roller coasters. How many roller coasters are in Hershey Park?

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4.1 – Fractions and Mixed Numbers Fractions Defn: Numbers that show the number of parts existing...

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