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**1.2 Fractions 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. Copyright © 2011 Pearson Education, Inc.

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Fractions Numerator Denominator Part Whole

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Equivalent Fractions ∙ 2 ∙ 2 ∙ 3 ∙ 3 ÷ 3 ∙ 2 ÷ 3 ∙ 2

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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,… Prime factorization: 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.

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**Find the prime factorization of 20.**

Factor Tree Factor Tower Divide by prime numbers! 2, 3, 5, 7, 11, …

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0, 2, 4, 6, 8 259: = 16 372: = 12 5, 10, 15, 20, … 10, 20, 30, 40, …

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**Find the prime factorization of 60.**

Factor Tree Factor Tower

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**Find the prime factorization of 48.**

Factor Tree Factor Tower

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Find the LCD. Using Multiples 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 10: 10, 20, 30, 40, 50, 60 LCD = 30 Use when numbers are small.

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**Using Prime Factorization**

Find the LCD. Using Prime Factorization 2∙3 2∙5 2 ∙ 3 ∙ 5 = 30 LCD:

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Find the LCD. Using Multiples 12: 12, 24, 36, 48, 60 9: 9, 18, 27, 36 LCD = 36

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**Using Prime Factorization**

Find the LCD. Using Prime Factorization 2∙2∙3 3∙3 LCD: 2∙2∙3 ∙ 3 = 36

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**Write the fractions as equivalent fractions with the LCD.**

24 ∙3 ∙2

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**Write the fractions as equivalent fractions with the LCD.**

Suggestion: 2∙2∙2∙2 2∙2∙3∙3 LCD: 2∙2∙2∙2∙3∙3 = 144 ∙9 ∙4

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**Reduce Fractions. GCF: 3 Using Prime Factorization**

Using Greatest Common Factor GCF: 3 3 4

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**Reduce Fractions. GCF: 6 Using Greatest Common Factor 5 7**

Using Prime Factorization

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**Reduce Fractions. GCF: ? Common Factor: 10 Common Factor: 2**

Using Greatest Common Factor Common Factor: 10 Common Factor: 2 11 119 Using Prime Factorization

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**Answer 3 out of 14 employees have optional eye insurance.**

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? ÷ 5 ÷ 5 ÷ 3 Answer 3 out of 14 employees have optional eye insurance.

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Simplifying Fractions

Simplifying Fractions

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