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.

ba

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

52

          

   

                        

85

127

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

107

53

65

4.1 – Fractions and Mixed NumbersDraw and shade each fraction.

73

              

              

              

              

                            

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 NumbersClassify each of the following fractions:

2923

715

8562

3347

954

61277

proper

proper

improper

improper

mixed number

mixed number

4.1 – Fractions and Mixed NumbersConverting Mixed Numbers to Improper Fractions

1. 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.

7257

725

7235

737

3263

326

3218

320

4.1 – Fractions and Mixed NumbersConverting Mixed Numbers to Improper Fractions

1071010

10710

107100

10107

1211812

12118

121196

12107

4.1 – Fractions and Mixed NumbersConverting Improper Fractions to Mixed Numbers

1. 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.

9559

54

1

54

1

4.1 – Fractions and Mixed NumbersConverting Improper Fractions to Mixed Numbers

239923

185

2

95

2

62131362

5210

4

1310

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 FormA 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 FormA 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

4530

533532

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

45

95

33

32

4.2 – Factors and Simplest FormSimplest Form

49

77

142

11249

7222277

Write in Simplest Form.

112

562

282

167

2 7

4.2 – Factors and Simplest FormSimplest Form

2064

16

2064

Write in Simplest Form.

5

16

5

common factor is 4

4.2 – Factors and Simplest FormSimplest Form

2

3

567aaa

2

3

567aa

Write in Simplest Form.

8a

8

common factor is 7a2

4.2 – Fractions and Simplest FormEquivalent Fractions – Two Methods

2721

97

7

997

97

?2721

97 equivalentandAre

1. Simplify each fraction. 2. Cross Multiply.

2721

97

189189

277219

Fractions are equivalent.

4.2 – Fractions and Simplest FormEquivalent Fractions – Two Methods

8534

156

52

52

175172

5332

?8534

156 equivalentandAre

1. Simplify each fraction. 2. Cross Multiply.

8534

156

510510

8563415

Fractions are equivalent.

4.2 – Fractions and Simplest FormEquivalent Fractions – Two Methods

185

3610

3912

134

332252

133322

?3610

3912 equivalentandAre

1. Simplify each fraction. 2. Cross Multiply.

3610

3912

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.

11753

115

73

7715

9311

91

31

271

4.3 – Multiplying and Dividing FractionsMultiplying Fractions

87776

87

776

3

41113

82734

83

274

2911

181

4

1

11443

1

2

1

9

4.3 – Multiplying and Dividing FractionsMultiplying Fractions

1611334

1633

114

1

4131

2332 y

23

32 y

1111 y y

4

3

143

1

1

1

1

4.3 – Multiplying and Dividing FractionsMultiplying Fractions

22

3

abba

22

3

ab

ba

a

11ba

43

43

43

3

43

3

3

43

6427

1

1

bba

4.3 – Multiplying and Dividing FractionsMultiplying Fractions

161062531

1625

103

61

1

1622511

2

5

2645

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.

12

94

21

94

98

25

78

52

78

1754

4

1

720

4.3 – Multiplying and Dividing FractionsDividing Fractions

29

410

92

410

445

351

43

yy35

43 yy

254113y

1

2y

2203y

1495

5

1

4.3 – Multiplying and Dividing FractionsDividing Fractions

715

149

32

157

149

32

4945

92

43

29

43

3211

1

3

61

7711531

1

7

3

1

.29

43, yandxifyxexpressiontheEvaluate

1

2

4.3 – Multiplying and Dividing FractionsDividing Fractions

715

149

32

157

149

32

4945

49

89

12

49

892

4

94191

1

4

49

49

7711531

1

7

3

1

?492

89

xequationtheofsolutionaIs YES

4.3 – Multiplying and Dividing FractionsDividing Fractions

160

6160

61

11101

10

110

6061 of

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?

coastersroller