Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 364: 126


The provided statement makes sense.

Work Step by Step

It is easy to solve equations that do not contain fractions. If some equation contains fraction it is better to remove it as early as possible since in that way it makes the steps simpler and approaches to solution quickly. Given equation\[0.5x+8.3=12.4\]contains decimal number as constants and coefficient of variable term x. Decimal number is nothing but another form of fraction number. For example, constant decimal terms and another coefficient term in the equation\[0.5x+8.3=12.4\]can be represented as\[0.5=\frac{5}{10},8.3=\frac{83}{10},12.4=\frac{124}{10}\]. Thus equation\[0.5x+8.3=12.4\] can be re-written as; \[\frac{5}{10}x+\frac{83}{10}=\frac{124}{10}\] This equation now contains fractions. To solve equation this fraction part needs to be clear from this equation. For this multiply both sides of the resulted equation by 10 gives \[\begin{align} & 10\left( \frac{5}{10}x+\frac{83}{10} \right)=10\left( \frac{124}{10} \right) \\ & 10\cdot \frac{5}{10}x+10\cdot \frac{83}{10}=10\cdot \frac{124}{10} \\ & 5x+83=124 \end{align}\] Fractions are cleared from the equation in three difficult steps. Now, see another point of view given in the statement. Just multiply both sides of the equation\[0.5x+8.3=12.4\] by 10 and get \[\begin{align} & 10\left( 0.5x+8.3 \right)=10\times 12.4 \\ & 10\left( 0.5x \right)+10\left( 8.3 \right)=124 \\ & 5x+83=124 \end{align}\] This way is much simpler and faster. Thus difference between both the points of view in the statement is clear. Thus points of view that multiply both sides of the equation\[0.5x+8.3=12.4\] by 10 are better option and thus make sense. Thus,the given statement that, “Because I know how to clear an equation of fractions, I decided to clear the equation \[0.5x+8.3=12.4\]of decimals by multiplying both sides by 10.” makes sense.
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