1. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers 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 California Standards

2. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers VOCABULARY CARDS Numerator Denominator Equivalent Fractions Improper Fraction Mixed Number Simpliest Form

3. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Different fractions can name the same number. 3535 = = 15 25 6 10

4. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers = To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number. In the diagram =. These are called equivalent fractions because they are different expressions for the same nonzero number. 3535 6 10 15 25

5. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Find two fractions equivalent to. Teacher Example 1: Finding Equivalent Fractions 5757 5  2 7  2 = 10 14 Multiply the numerator and denominator by 2. 5  3 7  3 = 15 21 Multiply the numerator and denominator by 3. Remember! A fraction with the same numerator and denominator, such as is equal to 1. 2

6. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers 5757 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. 5757 10 14 15 21

7. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Student Practice 1: Find two fractions equivalent to. 6  2 12  2 = 12 24 Multiply the numerator and denominator by 2. 6 ÷ 2 12 ÷ 2 = 3636 Divide the numerator and denominator by 2. 6 12

8. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Write the fraction in simplest form. Teacher Example 2: Writing Fractions in Simplest Form 18 24 Find the GCD of 18 and 24. The GCD is 6 = 2 3. = 18 24 Divide the numerator and denominator by 6. 18 = 2 3 3 24 = 2 2 2 3 18 ÷ 6 24 ÷ 6 = 3 4

9. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Write the fraction in simplest form. Student Practice 2: 15 45 Find the GCD of 15 and 45. The GCD is 15 = 3 5. = 15 45 Divide the numerator and denominator by 15. 15 = 3 5 45 = 3 3 5 15 ÷ 15 45 ÷ 15 = 1 3

10. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers To determine if two fractions are equivalent, simplify the fractions.

11. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Determine whether the fractions in each pair are equivalent. Teacher Example 3A: Determining Whether Fractions are Equivalent and 4646 28 42 Simplify both fractions and compare. 4646 = 4 ÷ 2 6 ÷ 2 = 2323 28 42 = 28 ÷ 14 42 ÷ 14 = 2323 are equivalent because both are equal to.and 4646 28 42 2323

12. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Teacher Example 3B: Determine whether the fractions in each pair are equivalent. and 6 10 20 25 Simplify both fractions and compare. = 6 ÷ 2 10 ÷ 2 = 3535 20 25 = 20 ÷ 5 25 ÷ 5 = 4545 6 10 are not equivalent because their simplestand 20 25 6 10 forms are not equal.

13. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Student Practice 3A: Simplify both fractions and compare. 3939 = 3 ÷ 3 9 ÷ 3 = 1313 = 6 ÷ 6 18 ÷ 6 = 1313 and 3939 6 18 6 18 Determine whether the fractions in each pair are equivalent. are equivalent because both are equal to.and 3939 6 18 1313

14. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Student Practice 3B: and 4 12 9 48 Simplify both fractions and compare. = 4 ÷ 4 12 ÷ 4 = 1313 9 48 = 9 ÷ 3 48 ÷ 3 = 3 16 4 12 Determine whether the fractions in each pair are equivalent. are not equivalent because their simplestand 9 48 4 12 forms are not equal.

15. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers 8585 = 1 3535 8585 is an improper fraction. Its numerator is greater than its denominator. 1 3535 is a mixed number. It contains both a whole number and a fraction.

16. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers 4A. Write Teacher Example 4: Converting Between Improper Fractions and Mixed Numbers 13 5 as a mixed number. First divide the numerator by the denominator. 13 5 = 2 3535 Use the quotient and remainder to write the mixed number. 4B. Write 7 2323 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. 23  + = 3  7 + 2 3 = 23 3 Use the result to write the improper fraction.

17. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Student Practice 4: 4A. Write 15 6 as a mixed number. First divide the numerator by the denominator. 15 6 = 2 3636 Use the quotient and remainder to write the mixed number. 4B. Write 8 1313 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. 13 8  + = 3  8 + 1 3 = 25 3 Use the result to write the improper fraction. 1212 = 2

18. Holt CA Course 1 3-4 Equivalent Fractions and Mixed Numbers Lesson Quiz 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. 12 24 16 48 3737 31 7 1818 2 17 8 1313 no 1212 3636, 5 12 4 10