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: 126


For 24 brownies, we need: 1 cup of butter 7$\frac{1}{2}$ ounces of unsweetened chocolate 2$\frac{1}{4}$ cups of sugar 3 teaspoons of vanilla 3 eggs 1$\frac{1}{2}$ cups of flour

Work Step by Step

To convert the recipe for 16 brownies to one that makes 24 brownies, we multiply the amount of each ingredient given for 16 brownies by $\frac{24}{16}$ = $\frac{3}{2}$ (in reduced form). Note 1: All mixed numerals must be converted to an improper fraction prior to multiplying. For example, the 1$\frac{1}{2}$ cups of sugar must be rewritten as the improper fraction of $\frac{3}{2}$. Note 2: Whole numbers, such as 2, must be written as $\frac{2}{1}$ before multiplying. Butter: $\frac{2}{3}$ x $\frac{3}{2}$ = $\frac{6}{6}$ = 1 cup Unsweetened Chocolate: $\frac{5}{1}$ x $\frac{3}{2}$ = $\frac{15}{2}$ = 7$\frac{1}{2}$ ounces (Note: This could also be written in decimal format at 7.5 ounces) Sugar: $\frac{3}{2}$ x $\frac{3}{2}$ = $\frac{9}{4}$ = 2$\frac{1}{4}$ cups Vanilla: $\frac{2}{1}$ x $\frac{3}{2}$ = $\frac{6}{2}$ = 3 teaspoons Eggs: $\frac{2}{1}$ x $\frac{3}{2}$ = $\frac{6}{2}$ = 3 eggs Flour: $\frac{1}{1}$ x $\frac{3}{2}$ = $\frac{3}{2}$ = 1$\frac{1}{2}$ cups
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