Holt CA Course 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

Holt CA Course Equivalent Fractions and Mixed Numbers VOCABULARY CARDS Numerator Denominator Equivalent Fractions Improper Fraction Mixed Number Simpliest Form

Holt CA Course Equivalent Fractions and Mixed Numbers Different fractions can name the same number = =

Holt CA Course 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

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

Holt CA Course 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

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

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

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

Holt CA Course Equivalent Fractions and Mixed Numbers To determine if two fractions are equivalent, simplify the fractions.

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

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

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

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

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

Holt CA Course 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 = Use the quotient and remainder to write the mixed number. 4B. Write as an improper fraction. First multiply the denominator and whole number, and then add the numerator. 23  + = 3  = 23 3 Use the result to write the improper fraction.

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

Holt CA Course 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 no ,