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Fractions1.21.2

1. Write equivalent fractions.2. Write equivalent fractions with the LCD.3. Write the prime factorization of a number.4. Simplify a fraction to lowest terms.

3

4

Numerator

Denominator

Part

Whole

Fractions

Equivalent Fractions

64

32

16?

83

166

?9

3027

109

96

32

∙ 2

∙ 2

∙ 3

∙ 3

∙ 2

∙ 2

÷ 3

÷ 3

Prime factorization:

Factors: Expressions that are being multiplied.

Prime number: A natural number that has only 1 and the number itself as factors.

2, 3, 5, 7, 11, 13, 17, 19, 23,…

A factorization that contains only prime factors.

1, 2, 3, 4, 6 and 12 are factors of 12.

Prime factorization of 12 is 2 ∙ 2 ∙ 3.

10202 20102202

Divide by prime numbers!

2, 3, 5, 7, 11, …

Find the prime factorization of 20.

20

54

522

Factor Tree Factor Tower

5102202

0, 2, 4, 6, 8

372: 3 + 7 + 2 = 12

5, 10, 15, 20, …

10, 20, 30, 40, …

259: 2 + 5 + 9 = 16

Find the prime factorization of 60.

60

106

5232

Factor Tree Factor Tower

5322

30602

15302602

5153302602 60

Find the prime factorization of 48.

48

86

4232

Factor Tree Factor Tower

32222

22232 24482

12242482

6122242482 48

362

122242482

Find the LCD.

103

and 65

6, 12, 18, 24, 30, 36, 42, 48, 54, 606:

10, 20, 30, 40, 50, 6010:

LCD = 30

Using Multiples

Use when numbers are small.

2∙3 2∙5

LCD: 2 ∙ 3 ∙ 5 = 30

103

and 65

Find the LCD.Using Prime Factorization

Find the LCD.

12, 24, 36, 48, 6012:

9, 18, 27, 369:

LCD = 36

Using Multiples

92

125

and

Find the LCD.Using Prime Factorization

92

125

and

2∙2∙3 3∙3

LCD: ∙ 3 = 362∙2∙3

Write the fractions as equivalent fractions with the LCD.

127

85

and

LCD: 24

127

85

and

2485

24127 24

1585

2414

127

∙3∙2

Write the fractions as equivalent fractions with the LCD.

LCD: 2∙2∙2∙2∙3∙3

367

165 and

144165

144367 144

45165

14428

367

2∙2∙2∙2 2∙2∙3∙3

∙9 ∙4

= 144

367

165

and

Suggestion:

Reduce Fractions.Using Prime Factorization

129 33

32233

43

129

Using Greatest Common Factor GCF: 3

3

443

30

42

Reduce Fractions.

Using Prime Factorization

Using Greatest Common Factor

30

42

2 3 5

2 3 7

5

7

5

7

5

7

GCF: 6

220

2380

2 2 5 11

2 2 5 7 17

11

119

Reduce Fractions.

Using Prime Factorization

Using Greatest Common Factor

GCF: Common Factor: 10

11

119

2380220

23822

Common Factor: 2

11911

?

At a company, 225 of the 1050 employees have optional eye insurance coverage as part of their benefits package. What fraction of the employees have optional eye insurance coverage?

Answer 3 out of 14 employees have optional eye insurance.

225

1050

÷ 5

21045

÷ 5

429

÷ 3

143

225

1050

3 3 5 5

2 3 5 5 7

3

14