## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 5 - Number Theory and the Real Number System - 5.5 Real Numbers and Their Properties; Clock Addition - Exercise Set 5.5 - Page 310: 75

#### Answer

(a) According to the distributive property of addition, $a\left( b+c \right)=ab+ac$ Use the above property in the given formula, \begin{align} & \frac{D\left( A+1 \right)}{24}=\frac{D\cdot A+D\cdot 1}{24} \\ & =\frac{DA+D}{24} \end{align} Both formulae are same as shown above. (b) Substitute $200$ for $D$ and $12$ for $A$ in the first formula. \begin{align} & \frac{D\left( A+1 \right)}{24}=\frac{200\left( 12+1 \right)}{24} \\ & =\frac{200\left( 13 \right)}{24} \\ & =108.33 \\ & \approx 108 \end{align} Substitute $200$ for $D$ and $12$ for $A$ in the second formula. \begin{align} & \frac{DA+D}{24}=\frac{200\cdot 12+200}{24} \\ & =\frac{2400+200}{24} \\ & =108.33 \\ & \approx 108 \end{align} With both expressions, the proper dose is approximately$108\,\text{mg}$. It is easier to use the first formula as an additional step of addition is reduced.

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