3 R.1 Fractions, Decimals, and Percents EXAMPLE 2 Converting an Improper Fraction to a Mixed Number Write 59 8 as a mixed number. SOLUTION Because the fraction bar represents division Qa b = a , b, or b)aR, divide the numerator of the improper fraction by the denominator. Denominator of fraction 7 8)59 56 3 Quotient Numerator of fraction Remainder 59 8 = 7 3 8 S Now Try Exercise 17. EXAMPLE 3 Converting a Mixed Number to an Improper Fraction Write 6 4 7 as an improper fraction. SOLUTION Multiply the denominator of the fraction by the natural number, and then add the numerator to obtain the numerator of the improper fraction. 7 # 6 = 42 and 42 + 4 = 46 The denominator of the improper fraction is the same as the denominator in the mixed number, which is 7 here. 6 4 7 = 7 # 6 + 4 7 = 46 7 S Now Try Exercise 21. Improper Fractions and Mixed Numbers A mixed number is a single number that represents the sum of a natural (counting) number and a proper fraction. Mixed number 2 3 4 = 2 + 3 4 Operations with Fractions Figure 2 illustrates multiplying fractions. of is equivalent to ∙ , which equals of the circle. 3 8 3 4 1 2 3 4 1 2 1 2 Figure 2 Multiplying Fractions If a b and c d are fractions 1b≠0, d≠02, then a b # c d = a # c b # d . That is, to multiply two fractions, multiply their numerators and then multiply their denominators.
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