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: 124


To make 12 brownies, you need: $\frac{1}{2}$ cup of butter, 3$\frac{3}{4}$ ounces of unsweetened chocolate, 1$\frac{1}{8}$ cups of sugar, 1$\frac{1}{2}$ teaspoons of vanilla, 1$\frac{1}{2}$ eggs, and $\frac{3}{4}$ cup of flour

Work Step by Step

To make 12 brownies using a recipe designed to make 16 brownies, first divide 12 by 16. We get $\frac{3}{4}$. We need to multiply each ingredient measure for 16 brownies by $\frac{3}{4}$. To make 16 brownies, we need $\frac{2}{3}$ cup of butter. Adjusting for 12 brownies, we multiply $\frac{2}{3}$ by $\frac{3}{4}$. This means we need $\frac{6}{12}$ which reduces to $\frac{1}{2}$ cup butter. We need 5 ounces of unsweetened chocolate for 16 brownies. To adjust to 12 brownies, we multiply $\frac{5}{1}$ x $\frac{3}{4}$. This means we need 3$\frac{3}{4}$ (3.75 in decimal form) ounces of unsweetened chocolate. For 16 brownies, we need 1$\frac{1}{2}$ cups of sugar. We convert mixed numerals to improper fractions before we multiply. $\frac{3}{2}$ x $\frac{3}{4}$ = $\frac{9}{8}$ cup of sugar. This equals 1$\frac{1}{8}$ cups of sugar. We need 2 teaspoons of vanilla for 16 brownies. To make 12 brownies, we need $\frac{2}{1}$ x $\frac{3}{4}$ = $\frac{6}{4}$ = $\frac{3}{2}$, or 1.5 teaspoons of vanilla. For 16 brownies, 2 eggs are needed. To make 12 brownies, $\frac{2}{1}$ x $\frac{3}{4}$ which is $\frac{3}{2}$ or 1.5 eggs. Last, we need 1 cup of flour for 16 brownies. To adjust to 12 brownies, we multiply 1 by $\frac{3}{4}$ which means we need $\frac{3}{4}$ cup of flour.
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