Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Entry-Level Assessment - Multiple Choice - Page xxxix: 19


D; $6\frac{1}{6}$

Work Step by Step

To add fractions, we must first have a common denominator. The denominators of the three fractions in this problem are 4, 2, and 3. To find the lowest common denominator, list the multiples of each denominator. Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16... Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24... Multiples of 4: 4, 8, 12, 16, 20, 24, 28... The lowest number that is a multiple of all three denominators is 12; therefore, our lowest common denominator, or LCM, is 12. To change a fraction's denominator, we must also change its numerator. Multiply the numerator by the same number you multiplied the denominator by to turn your original denominator into your LCM. Then, add the numerators together, keeping the denominator the same. You do not add denominators when adding fractions. Finally, reduce the fraction. Following these steps in our problem gives us: $3\frac{3}{4}+1\frac{1}{2}+\frac{2}{3}+\frac{1}{4} =3\frac{3\times3}{4\times3}+1\frac{1\times6}{2\times6}+\frac{2\times4}{3\times4}+\frac{1\times3}{4\times3} =3\frac{9}{12}+1\frac{6}{12}+\frac{8}{12}+\frac{3}{12} =4\frac{26}{12} =6\frac{2}{12} =6\frac{1}{6}$
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