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: 136

Answer

$\frac{1}{4}$ of the workshop participants are writers.

Work Step by Step

At a workshop there are musicians, artists, actors, and writers. Musicians make up $\frac{1}{4}$ of the workshop participants. Artists make up $\frac{2}{5}$ of the workshop participants. Actors make up $\frac{1}{10}$ of the workshop participants. We need to find out what fractional part of the workshop participants are writers. The workshop participants all together can be considered 1 unit. We can set up an equation like this: Musicians + artists + actors + writers = 1 If we substitute each fractional part into our equations and let writers be equal to "x", we can solve and find the fractional part that is writers. So, we have the equation: $\frac{1}{4}$ + $\frac{2}{5}$ + $\frac{1}{10}$ + x = 1 Now we can find a common denominator for our fractions and write an equivalent fraction for each one using the common denominator. For the denominators of 4, 5, and 10, the least common denominator is 20. If we write each fraction using the denominator of 20, and write the whole number, one, as a fraction using the common denominator of 20, we have: $\frac{5}{20}$ + $\frac{8}{20}$ + $\frac{2}{20}$ + x = $\frac{20}{20}$ By adding the fractions (we only add the numerators, the denominator remains 20). We have: $\frac{15}{20}$ + x = $\frac{20}{20}$ We can now "Isolate" the variable "x" by subtracting $\frac{15}{20}$ from both sides of the equation. $\frac{15}{20}$ - $\frac{15}{20}$ + x = $\frac{20}{20}$ - $\frac{15}{20}$ and we get: x = $\frac{5}{20}$ = $\frac{1}{4}$ (reduced form) This shows us that $\frac{1}{4}$ of the workshop participants are writers.
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