Chapter 6.4, Problem 27E

To determine

To calculate: the simplest form of the fraction $\frac{24x}{60x^2{y}^3}$ .

Answer to Problem 27E

The simplest form of the fraction $\frac{24x}{60x^2{y}^3}$ is $\frac{2}{5x{y}^3}$ .

Explanation of Solution

Given information : the fractionis $\frac{24x}{60x^2{y}^3}$ .

Calculation : to find the simplest form of the fraction, first factor the numerator and denominator, then divide out the common factors, then simplify.

  $\begin{array}{l}\frac{24x}{60x^2{y}^3}=\frac{12·2·x}{12·5·x·x·y·y·y}\text{ [factor]}\\ \frac{24x}{60x^2{y}^3}=\frac{2}{5\cdot x·y·y·y}\text{ [divide out common factors]}\\ \frac{24x}{60x^2{y}^3}=\frac{2}{5x{y}^3}\text{ [simplify]}\end{array}$

Hence,Thesimplest form of the fraction $\frac{24x}{60x^2{y}^3}$ is $\frac{2}{5x{y}^3}$ .