Prealgebra (7th Edition)

Published by Pearson
ISBN 10: 0321955048
ISBN 13: 978-0-32195-504-3

Chapter 4 - Section 4.6 - Complex Fractions and Review of Order of Operations - Exercise Set: 57


$3\frac{1}{2}$, $\frac{7}{2}$

Work Step by Step

When a fraction has an integer value followed by a fraction where the numerator of the fraction is less than the denominator of the fraction i.e. $x\frac{y}{z}$ where 1) $x, y$ and $z, \ne0$ 2) $y, z \gt0$ 3) $y\lt z$ It is called a mixed number. When a fraction has no integer value before it and the numerator is greater than or equal to the denominator i.e. $\frac{y}{z}$ where 1) $y$ and $z \ne0$ 2) $y\geq z$ It is called an improper fraction. We can convert a mixed number ($x\frac{y}{z}$) to an improper fraction \frac{y}{z} using the following formula: $x\frac{y}{z}=\frac{xz+y}{z}$ In this problem, we can express $3+\frac{1}{2}$ as a mixed number by "removing" the plus sign (any integer plus a fraction can be expressed as a mixed number by simply removing the addition sign): $3\frac{1}{2}$ We can convert this to an improper fraction using the formula: $3\frac{1}{2}=\frac{(3)(2)+1}{2}$ $=\frac{6+1}{2}$ $=\frac{7}{2}$
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