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: 125

Answer

To make 20 brownies, we need $\frac{5}{6}$ cups of butter, 6$\frac{1}{4}$ or 6.25 ounces of unsweetened chocolate, 1$\frac{7}{8}$ cups of sugar, 2$\frac{1}{2}$ teaspoons of vanilla, 2$\frac{1}{2}$ eggs, and 1$\frac{1}{4}$ cups of flour.

Work Step by Step

The multiplier we need to convert the ingredient amounts from 16 brownies in the original recipe to 20 brownies is: $\frac{20}{16}$ or, in reduced form, $\frac{5}{4}$. Note: all mixed numerals must be converted to improper fractions prior to being multiplied. Butter: $\frac{2}{3}$ x $\frac{5}{4}$ which is $\frac{10}{12}$= $\frac{5}{6} cups$. Unsweetened chocolate: $\frac{5}{1}$ x $\frac{5}{4}$ which is $\frac{25}{4}$. This is 6$\frac{1}{4}$ or 6.25 ounces. NOTE: Before converting the amounts for sugar, we must first change 1$\frac{1}{2}$ cups to $\frac{3}{2}$ cups. Sugar: $\frac{3}{2}$ x $\frac{5}{4}$ which means we need $\frac{15}{8}$ = 1$\frac{7}{8}$ cups NOTE: Whole numbers are written over 1 so we can multiply them. Vanilla: $\frac{2}{1}$ x $\frac{5}{4}$ = $\frac{10}{4}$ = 2$\frac{1}{2}$ teaspoons. Eggs: $\frac{2}{1}$ x $\frac{5}{4}$ = $\frac{10}{4}$ = 2$\frac{1}{2}$ eggs. Flour: $\frac{1}{1}$ x $\frac{5}{4}$ = $\frac{5}{4}$ = 1$\frac{1}{4}$ cups.
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