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California Standards

Learn how to determine equivalent fractions and simplify fractions using the least common multiple and greatest common divisor. Practice converting between improper fractions and mixed numbers.

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California Standards

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  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

  2. Vocabulary equivalent fractions improper fraction mixed number Different expressions for the same nonzero number. (fractions that are equal to each other). A fraction in which the numerator is greater than the denominator. A number that contains a whole number and a fraction.

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

  4. 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.

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

  6. 15 21 5 7 10 14 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

  7. 18 ÷6 24 ÷ 6 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 3 4 Divide the numerator and denominator by 6. 1 = =

  8. You can also simplify fractions by dividing by common factors until the numerator and denominator have no more common factors except one. To determine if two fractions are equivalent, simplify the fractions.

  9. 4 6 28 42 2 3 and are equivalent because both are equal to . Additional Example 3A: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent. 4 6 28 42 and 4 6 Simplify both fractions and compare. 4 ÷ 2 6 ÷ 2 2 3 1 = = 28 ÷ 14 42 ÷ 14 28 42 2 3 1 = =

  10. 20 25 and are not equivalent because their simplest 6 10 forms are not equal. 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 ÷ 2 10 ÷ 2 6 10 3 5 1 = = 4 5 20 ÷ 5 25 ÷ 5 20 25 1 = =

  11. 3 5 8 5 is an improper 1 is a mixed fraction. Its numerator is greater than its denominator. number. It contains both a whole number and a fraction. 3 5 8 5 = 1

  12. Example 4: Converting Between Improper Fractions and Mixed Numbers as a mixed number. A. Write 13 5 First divide the numerator by the denominator. Use the quotient and remainder to write the mixed number. 3 5 13 5 = 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. 3 7 + 2 2 3 23 3 = = 7 3 

  13. 6 12 Check It Out! Example 1 Find two fractions equivalent to . 12 24 6 2 1 Multiply the numerator and denominator by 2. = 12 2 6 ÷ 2 12 ÷ 2 Divide the numerator and denominator by 2. 3 6 1 =

  14. 15 ÷15 45 ÷ 15 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 1 3 1 Divide the numerator and denominator by 15. = =

  15. 3 9 6 18 and 6 18 3 9 6 18 1 3 and are equivalent because both are equal to . Check It Out! Example 3A Determine whether the fractions in each pair are equivalent. Simplify both fractions and compare. 3 9 3 ÷ 3 9 ÷ 3 1 3 1 = = 6 ÷ 6 18 ÷ 6 1 3 1 = =

  16. 1 2 = 2 Check It Out! Example 4 15 6 as a mixed number. A. Write First divide the numerator by the denominator. Use the quotient and remainder to write the mixed number. 3 6 15 6 = 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. 3  8 + 1 1 3 25 3 = 8 = 3 

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