Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 286: 129


3$\frac{2}{3}$ cups of water is needed to make 11 servings of instant potatoes.

Work Step by Step

The problem states that 2$\frac{2}{3}$ cups of water is needed for 8 servings of instant potatoes. So, first we need to find the amount of water needed to make 1 serving of instant potatoes. To do this, we divide the amount of water (2$\frac{2}{3}$ cups) by the number of servings it makes (8 servings). Before completing any calculations, we need to convert mixed numeral to improper fractions and also be sure to note that whole numbers can be written as fractions by using the whole number as the numerator (top of fraction) and 1 as the denominator (bottom of fraction). 2$\frac{2}{3}$ = $\frac{8}{3}$ (Converting mixed numeral to improper fraction). 8 = $\frac{8}{1}$ (Writing whole number as a fraction). Also, remember the procedure for fraction division. We keep the first fraction as it is. We flip the second fraction over (or find its reciprocal). Last, we change the operation from division to multiplication. Now, find the amount of water needed to make one serving of potatoes. $\frac{8}{3}$ $\div$ $\frac{8}{1}$ = $\frac{8}{3}$ $\times$ $\frac{1}{8}$ = $\frac{8}{24}$ = $\frac{1}{3}$ This means we need $\frac{1}{3}$ cup of water for each serving of instant potatoes we want to make. So, if we want to make 11 servings of instant potatoes, we need to multiply 11 times $\frac{1}{3}$. $\frac{11}{1}$ $\times$ $\frac{1}{3}$ = $\frac{11}{3}$ cups of water needed for 11 servings of the potatoes. Converting this back to a mixed numeral, $\frac{11}{3}$ = 3$\frac{2}{3}$ cups of water.
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