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: 128


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. If such equation is represented in the form of two ratios equal to each other then it is better to use cross product principle to solve it. For example; If \[\frac{a}{b}=\frac{c}{d}\] then \[ad=bc\text{ where }b\ne 0\text{ and }d\ne 0\] The given equation\[\frac{x}{9}=\frac{4}{6}\] also represents two ratios equal to each other. Thus, if you know the rule then it is better to apply cross product principle to solve this equation. \[\frac{x}{9}=\frac{4}{6}\] Apply cross product principle gives \[6x=9.4\] Now, cross multiply then, \[6x=36\] Divide both sides by 6, \[\frac{6x}{6}=\frac{36}{6}\] Simplify it, \[x=6\] Now second point of view is to solve the same equation\[\frac{x}{9}=\frac{4}{6}\] by multiplying both sides by 18 the least common denominator will also solve the equation. But here one has to calculate the least common denominator first. Anyway, it hardly matters which way is chosen to solve the equation. It matters that method to solve the problem should be simpler and correct and above all it is correctly understandable by the user. Therefore, the given statement that, “I can solve \[\frac{x}{9}=\frac{4}{6}\]by using the cross products principle or by multiplying both sides by 18, the least common denominator.” makes sense.
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