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: 130

Answer

2 cups of water are needed to make 6 servings of instant potatoes.

Work Step by Step

In order to arrive at the answer of 2 cups of water, we first need to find the amount of water needed for one serving of instant potatoes. To do this, we use the information given in the problem: 2$\frac{2}{3}$ cups of water is needed to make 8 servings of instant potatoes. We can now divide the amount of water needed by the number of servings it makes. NOTE: Before we divide, we need to convert the 2$\frac{2}{3}$ to an improper fraction. The improper fraction we need is $\frac{8}{3}$. We also need to note that 8 (servings) can be written as a fraction by writing it as $\frac{8}{1}$. Now, we can divide $\frac{8}{3}$ by $\frac{8}{1}$ Remember the procedure for dividing fractions is to keep the first one as is (the $\frac{8}{3}$ stays as is). Then, we flip the second fraction. This is called finding the reciprocal. Then we find the reciprocal of $\frac{8}{1}$. In other words, flip it over and get $\frac{1}{8}$. Now change the division to multiplication. We have: $\frac{8}{3}$ $\times$ $\frac{1}{8}$ = $\frac{8}{24}$ = $\frac{1}{3}$ (reduced form) This means we need $\frac{1}{3}$ cup of water for each serving of the instant potatoes. Therefore, to make 6 servings, we need to multiply $\frac{1}{3}$ by 6. $\frac{1}{3}$ $\times$ $\frac{6}{1}$ = $\frac{6}{3}$ = 2 This gives us the solution of needing 2 cups of water to make six servings of instant potatoes.
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