Chapter 5.7, Problem 44E

To determine

Toexplain:Clear the fractions in an equation by multiplying each side of the equation by a common denominator other than the LCD.

Answer to Problem 44E

It is possible to clear the fractions in an equation by multiplying each side of the equation by a common denominator other than the LCD.

Explanation of Solution

Given information: Clear friction method.

Let there is equation $\frac{2}{3}x-1=\frac{5}{6}$ , clear the fractions of the equations

it is needed to multiply both side by common denominator $12$ other than the least common denominator which is $6$

  $\Rightarrow 12\times (\frac{2}{3}x-1)=\frac{5}{6}\times 12$

  $\text{Using}\text{distributive}\text{property}$ ,

  $\begin{array}{l}\Rightarrow 12\times \frac{2}{3}x-1\times 12=10\\ \Rightarrow 8x-12=10\end{array}$

  $\text{Add}12\text{in}\text{each}\text{side}$ ,

  $\begin{array}{l}\Rightarrow 8x-12+12=10+12\\ \Rightarrow 8x=22\end{array}$

  $\text{Divide}\text{each}\text{side}\text{by}8$ ,

  $\begin{array}{l}\Rightarrow \frac{8x}{8}=\frac{22}{8}\\ \Rightarrow x=\frac{11}{4}\end{array}$

Hence,

The solution of equation $\frac{2}{3}x-1=\frac{5}{6}$ is $x=\frac{11}{4}$

So, it is possible to clear the fractions in an equation by multiplying each side of the equation by a common denominator other than the LCD