Chapter 3.6, Problem 43PPS

To determine

To calculate: have to calculate the difference of the given fraction.

Answer to Problem 43PPS

The difference of the given fraction is $\left(\frac{-355}{6}\right)$ .

Explanation of Solution

Given data: $-35\frac{5}{6}-23.\overline{3}$

Some simple steps have to follow to add or subtract the, unlike fractions.

Sept-I:Convert Recurring numbers into the fractions.

Since, $23.\overline{3}$ is a recurring number mean that 23.33333333333

Suppose the $x=23.33333333\mathrm{...}\left(\text{i}\right)$

Now, multiply the equation (i) by 10 both side, we get

  $10x=233.3333333\mathrm{...}\left(\text{ii}\right)$

Subtract the equation (i) to equation (ii), we get

  $\begin{array}{l}\Rightarrow 9x=210\\ \Rightarrow x=\frac{210}{9}=\frac{70}{3}\end{array}$

Step-II: Convert the mixed fraction into an improper fraction (if any).

  $\begin{array}{l}=-35\frac{5}{6}-\frac{70}{3}\\ =-\frac{35\times 6+5}{6}-\frac{70}{3}\end{array}$

  $=-\frac{215}{6}-\frac{70}{3}$ [Unlike fraction]

Step-III: Calculate the ‘Least Common Multiple’ (LCM) of the denominator of the given fraction.

  $\begin{array}{cc}3& 6,3\\ & 2,1\end{array}$

Now, Least Common Multiple (LCM) $=2\times 3=6$

Step-IV: Convert each fraction into an equivalent fraction by multiplies and divide of its denominator and numerator to the equal to the ‘Least Common Multiple’ (LCM) obtained in step -II.

  $\begin{array}{l}=-\frac{215}{6}-\frac{70}{3}\\ =-\frac{215\times 1}{6\times 1}-\frac{70\times 2}{3\times 2}\end{array}$

  $=-\frac{215}{6}-\frac{140}{6}$ [Like fraction]

Step-V: Add or subtract the like fraction to convert into a simple form.

  $\begin{array}{l}=-\frac{215}{6}-\frac{140}{6}\\ =\frac{-215-140}{6}\\ =\frac{-355}{6}\end{array}$