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Preview Warm Up California Standards Lesson Presentation

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Warm Up Name a common factor for each pair. 1. 5 and and 12 3. 20 and and 14 5. 6 and and 15 Possible answers: 5 3 4 2 2 1

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California Standards Number Sense (NS2.4) - Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form of a fraction). Also covered: Number Sense (NS1.1)

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Vocabulary equivalent fractions improper fraction mixed number

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**Different fractions can name the same number.**

3 5 6 10 15 25 = =

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**In the diagram = . These are called **

equivalent fractions because they are different expressions for the same nonzero number. = To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.

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**Find two fractions equivalent to .**

Additional Example 1: Finding Equivalent Fractions 5 7 Find two fractions equivalent to . 5 2 10 14 = Multiply the numerator and denominator by 2. 7 2 5 3 15 21 = Multiply the numerator and denominator by 3. 7 3 Remember! A fraction with the same numerator and denominator, such as is equal to 1. 2 2

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5 7 10 14 15 21 The fractions , , and are equivalent, but only is in simplest form. A fraction is in simplest form when the greatest common divisor of its numerator and denominator is 1. 5 7

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**Find two fractions equivalent to .**

Check It Out! Example 1 6 12 Find two fractions equivalent to . 6 2 12 24 = Multiply the numerator and denominator by 2. 12 2 6 ÷ 2 12 ÷ 2 3 6 = Divide the numerator and denominator by 2.

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**Additional Example 2: Writing Fractions in Simplest Form**

18 24 Write the fraction in simplest form. Find the GCD of 18 and 24. 18 = 2 • 3 • 3 The GCD is 6 = 2 • 3. 24 = 2 • 2 • 2 • 3 18 24 18 ÷ 6 24 ÷ 6 3 4 = = Divide the numerator and denominator by 6.

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**Write the fraction in simplest form.**

Check It Out! Example 2 15 45 Write the fraction in simplest form. Find the GCD of 15 and 45. 15 = 3 • 5 The GCD is 15 = 3 • 5. 45 = 3 • 3 • 5 15 45 15 ÷ 15 45 ÷ 15 1 3 = = Divide the numerator and denominator by 15.

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**To determine if two fractions are equivalent, simplify the fractions.**

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**Additional Example 3A: Determining Whether Fractions are Equivalent**

Determine whether the fractions in each pair are equivalent. 4 6 28 42 and Simplify both fractions and compare. 4 6 4 ÷ 2 6 ÷ 2 2 3 = = 28 42 28 ÷ 14 42 ÷ 14 2 3 = = 4 6 28 42 2 3 and are equivalent because both are equal to .

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**Additional Example 3B: Determining Whether Fractions are Equivalent**

Determine whether the fractions in each pair are equivalent. 6 10 20 25 and Simplify both fractions and compare. 6 10 6 ÷ 2 10 ÷ 2 3 5 = = 20 25 20 ÷ 5 25 ÷ 5 4 5 = = are not equivalent because their simplest and 20 25 6 10 forms are not equal.

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Check It Out! Example 3A Determine whether the fractions in each pair are equivalent. and 3 9 6 18 Simplify both fractions and compare. 3 9 3 ÷ 3 9 ÷ 3 1 3 = = 6 18 6 ÷ 6 18 ÷ 6 1 3 = = 3 9 6 18 1 3 and are equivalent because both are equal to .

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Check It Out! Example 3B Determine whether the fractions in each pair are equivalent. 4 12 9 48 and Simplify both fractions and compare. 4 12 4 ÷ 4 12 ÷ 4 1 3 = = 9 48 9 ÷ 3 48 ÷ 3 3 16 = = are not equivalent because their simplest and 9 48 4 12 forms are not equal.

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**8 3 = 1 5 5 8 5 3 5 is an improper 1 is a mixed fraction. Its**

numerator is greater than its denominator. 8 5 3 5 number. It contains both a whole number and a fraction. = 1

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** (A) Write as a mixed number.**

Additional Example 4: Converting Between Improper Fractions and Mixed Numbers (A) Write 13 5 as a mixed number. First divide the numerator by the denominator. 13 5 3 5 Use the quotient and remainder to write the mixed number. = 2 2 3 (B) Write 7 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. + 2 3 3 7 + 2 23 3 = Use the result to write the improper fraction. = 7 3

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**8 Check It Out! Example 4 (A) Write as a mixed number.**

15 6 (A) Write as a mixed number. First divide the numerator by the denominator. 15 6 3 6 = 2 1 2 = 2 Use the quotient and remainder to write the mixed number. 1 3 (B) Write 8 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. + 1 3 3 8 + 1 Use the result to write the improper fraction. 25 3 8 = = 3

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**1. Write two fractions equivalent to . **

Lesson Quiz 1 2 3 6 , 12 24 1. Write two fractions equivalent to 2. Determine if and are equivalent. 3. Write the fraction in simplest form. 4. Write as a mixed number. 5. Write 4 as an improper fraction. 5 12 4 10 no 16 48 1 3 17 8 1 8 2 3 7 31 7

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