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Version 7/2/2016 Hanh X. Vo Division of Mixed Numbers I. Introduction: We will explain how to divide mixed numbers by a fraction, a whole number, or another mixed number in this section. II. How to Divide Mixed Numbers: 1) Dividing a Mixed Number by a Fraction: Follow these simple steps: Convert the mixed number to improper fraction Find the reciprocal of the fraction Multiply the numerators Multiply the denominators Convert the result to mixed number as needed Simplify the fraction part as needed Example 1: 1 3 Find 8 1 2 Let’s convert the mixed number to improper fraction (See To_Improp): 1 8 3 1 25 8 3 3 3 The reciprocal of 1 2 is 2 or (See Reciprocal) 2 1 Multiply the two fractions: 25 2 25 2 50 3 1 3 1 3 Since 50 is an improper fraction, let’s convert it to mixed number (See To_Mixed): 3 1 Version 7/2/2016 Hanh X. Vo 50 2 16 3 3 Thus, 1 1 2 8 16 3 2 3 Example 2: Find 3 1 2 2 5 Let’s convert the mixed number to improper fraction (See To_Improp): 1 3 2 1 7 3 2 2 2 The reciprocal of 2 5 is (See Reciprocal) 5 2 Multiply the two fractions: 7 5 7 5 35 2 2 2 2 4 Since 35 is an improper fraction, let’s convert it to mixed number (See To_Mixed): 4 35 3 8 4 4 Thus, 1 2 3 3 8 2 5 4 2 Version 7/2/2016 Hanh X. Vo 2) Dividing a Mixed Number by a Whole Number: Note that a whole number can be written as a fraction with the denominator as 1: For example: 6 6 15 3 ; 15 ; 3 1 1 1 Thus, we can apply the same steps shown above for this situation. Example 1: 1 3 Find 8 2 Let’s convert the mixed number to improper fraction (See To_Improp): 1 8 3 1 25 8 3 3 3 And, the whole number 2 can be written as So, the reciprocal of 2 1 2 1 is (See Reciprocal) 1 2 Multiply the two fractions: 25 1 25 1 25 3 2 3 2 6 25 is an improper fraction, let’s convert it to mixed number (See To_Mixed): 6 25 1 4 6 6 Since Thus, 1 1 8 24 3 6 Example 2: 3 Version 7/2/2016 Hanh X. Vo Find 5 1 3 4 Let’s convert the mixed number to improper fraction (See To_Improp): 1 5 4 1 21 5 4 4 4 And, the whole number 3 can be written as So, the reciprocal of 3 1 3 1 is (See Reciprocal) 1 3 Multiply the two fractions: 21 1 21 1 21 4 3 4 3 12 The GCF of 21 and 12 is 3 (See Greatest Common Factor GCF) The above result can be further simplified as: 21 21 3 7 12 12 3 4 7 is an improper fraction, let’s convert it to mixed number (See To_Mixed): 4 7 3 1 4 4 Since Thus, 1 3 5 3 1 4 4 3) Dividing a Mixed Number by Another Mixed Number: Follow these simple steps: Convert the first mixed number to improper fraction Convert the second mixed number to improper fraction 4 Version 7/2/2016 Hanh X. Vo Find the reciprocal of the second improper fraction Multiply the numerators Multiply the denominators Convert the result to mixed number as needed Simplify the fraction part as needed Example 1: 5 8 Find 5 2 1 2 Convert the first mixed number to improper fraction (See To_Improp): 5 5 8 5 45 5 8 8 8 Convert the second mixed number to improper fraction (See To_Improp): 1 2 2 1 5 2 2 2 2 The reciprocal of 5 2 is (See Reciprocal) 2 5 Multiply the two fractions: 45 2 45 2 90 9 8 5 8 5 40 4 Since 9 is an improper fraction, let’s convert it to a mixed number (See To_Mixed): 4 9 1 2 4 4 Thus, 5 1 1 5 2 2 8 2 4 5 Version 7/2/2016 Hanh X. Vo Example 2: 1 3 Find 3 2 3 5 Convert the first mixed number to improper fraction (See To_Improp): 1 3 3 1 10 3 3 3 3 Convert the second mixed number to improper fraction (See To_Improp): 3 2 5 3 13 2 5 5 5 The reciprocal of 13 5 is (See Reciprocal) 5 13 Multiply the two fractions: 10 5 10 5 50 3 13 3 13 39 Since 50 is an improper fraction, let’s convert it to a mixed number (See To_Mixed): 39 50 11 1 39 39 Thus, 1 3 11 3 2 1 3 5 39 6