Preview Warm Up California Standards Lesson Presentation

Warm Up Name a common factor for each pair. 1. 5 and 10 2. 9 and 12 3. 20 and 24 4. 10 and 14 5. 6 and 8 6. 8 and 15 Possible answers: 5 3 4 2 2 1

California Standards 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: NS1.1

Vocabulary equivalent fractions improper fraction mixed number

Different fractions can name the same number. 3 5 6 10 15 25 = =

In the diagram = . These are called equivalent fractions because they are different expressions for the same nonzero number. 3 5 6 10 15 25 = To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.

Additional Example 1: Finding Equivalent Fractions 5 7 Find two fractions equivalent to . 5  2 1 10 14 = Multiply the numerator and denominator by 2. 7  2 5  3 1 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

5 7 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 10 14 15 21

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

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 1 Divide the numerator and denominator by 6. = =

1 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 1 Divide the numerator and denominator by 15. = =

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

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 1 2 3 = = 28 42 28 ÷ 14 42 ÷ 14 2 3 = 1 = are equivalent because both are equal to . and 4 6 28 42 2 3

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 1 3 5 = = 20 25 20 ÷ 5 25 ÷ 5 4 5 1 = = are not equivalent because their simplest and 20 25 6 10 forms are not equal.

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 1 = = 6 18 6 ÷ 6 18 ÷ 6 1 3 1 = = are equivalent because both are equal to . and 3 9 6 18 1

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 1 3 = = 9 48 9 ÷ 3 48 ÷ 3 1 3 16 = = are not equivalent because their simplest and 9 48 4 12 forms are not equal.

8 5 3 5 = 1 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

 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. + Use the result to write the improper fraction. 2 3 3  7 + 2 23 3 = = 7 3 

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 1 2 = 2 Use the quotient and remainder to write the mixed number. = 2 1 3 B. Write 8 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. + Use the result to write the improper fraction. 1 3 3  8 + 1 25 3 8 = = 3 

1. Write two fractions equivalent to . Lesson Quiz 12 24 1 2 3 6 , 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