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 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)

Objective: You will learn how to identify, write, and convert between equivalent fractions and mixed numbers.

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. = To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.

Find two fractions equivalent to . Example 1: Finding Equivalent Fractions 57 Find two fractions equivalent to . 5  2 10 14 = Using “Cake” 7  2 5  3 15 21 = 7  3 Remember! A fraction with the same numerator and denominator, such as is equal to 1. 2 2

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

Check It Out! Example 2 6 12 Find two fractions equivalent to . Using “Cake” 6  2 12 24 = 12  2 6 ÷ 2 12 ÷ 2 3 6 =

Example 3: Writing Fractions in Simplest Form 18 24 Write the fraction in simplest form. Using Factors Using “Cake”

Check It Out! Example 4 15 45 Write the fraction in simplest form. Using Factors Using “Cake”

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

Example 5: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 4 6 28 42 and Simplify both fractions and compare. Using “Cake” 4 6 4 ÷ 2 6 ÷ 2 2 3 = = 28 42 28 ÷ 14 42 ÷ 14 2 3 = = 4 6 28 42 and are equivalent because both are equal to . 2 3

Example 5: Comparing Using Cross-Products Determine whether the fractions in each pair are equivalent. 4 6 28 42 and

Example 6: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 6 10 20 25 and Using “Cake” 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 and 20 25 6 10 their simplest forms are not equal.

Example 6: Comparing Using Cross-Products Determine whether the fractions in each pair are equivalent. 6 10 20 25 and

Check It Out! Example 7 Determine whether the fractions in each pair are equivalent. and 3 9 6 18 Simplify both fractions and compare. Using “Cake” 3 9 3 ÷ 3 9 ÷ 3 1 3 = = 6 18 6 ÷ 6 18 ÷ 6 1 3 = = 3 9 6 18 and are equivalent because both are equal to . 1 3

Example 7: Comparing Using Cross-Products Determine whether the fractions in each pair are equivalent. and 3 9 6 18 19

Check It Out! Example 8 Determine whether the fractions in each pair are equivalent. 4 12 9 48 and Using “Cake” 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 and 9 48 4 12 their simplest forms are not equal.

Example 8: Comparing Using Cross-Products Determine whether the fractions in each pair are equivalent. 4 12 9 48 and 21

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

Example 9: 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 

8  Check It Out! Example 10 (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 

Home Learning On-Line Tutoring Melvin’s Dilemma Equivalent Fractions?

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