# Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3: 127

WIth 1 cup of butter, you can make 24 total (whole) brownies.

#### Work Step by Step

If $\frac{2}{3}$ cup of butter will make 16 brownies, then 1 cup of butter makes 24 brownies. We get 24 by setting up a ratio of 16 brownies to $\frac{2}{3}$ cup of butter. This ratio is 16 $\div$ $\frac{2}{3}$ In fraction division, we keep the first number (in our case 16), flip the second number (in our case, we flip $\frac{2}{3}$ and get $\frac{3}{2}$) and we change the $\div$ sign to a $\times$ sign. In other words, we multiply by the reciprocal of the second fraction. Thus, we have: $\frac{16}{1}$ x $\frac{3}{2}$ = $\frac{48}{2}$ = 24. 24 times the 1 cup of butter given still gives us 24. Therefore, 24 brownies can be made with 1 cup of butter.

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