Chapter 3.6, Problem 52HP

To determine

To Justify:When we solve the difference between $\left(2\frac{3}{4}-5\frac{5}{6}\right)$ , the same answer will be, if we use 24 instead of 12 as a common denominator.

Explanation of Solution

Given data: $2\frac{3}{4}-5\frac{5}{6}$

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

Step -I: Convert the Mixed fraction into an improper fraction (if any).

  $\begin{array}{l}=2\frac{3}{4}-5\frac{5}{6}\\ =\frac{2\times 4+3}{4}-\frac{5\times 6+5}{6}\end{array}$

  $=\frac{11}{4}-\frac{35}{6}$ [Unlike fraction]

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

$\begin{array}{cc}2& 4,6\\ & 2,3\end{array}$

Now, Least Common Multiple (LCM) $=2\times 2\times 3=12$

Step -III: 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.

  $\begin{array}{l}=\frac{11}{4}-\frac{35}{6}\\ =\frac{11\times 3}{4\times 3}-\frac{35\times 2}{6\times 2}\end{array}$

  $=\frac{33}{12}-\frac{70}{12}$ [Like fraction]

Step −IV: Add or subtract the like fraction to convert into a simple form.

  $\begin{array}{l}=\frac{33}{12}-\frac{70}{12}\\ =\frac{33-70}{12}\\ =\frac{-37}{12}\end{array}$

As per the question use 24 instead of 12 as a common denominator.

Therefore, $=\frac{33}{24}-\frac{70}{24}$

  $\begin{array}{l}=\frac{33}{24}-\frac{70}{24}\\ =\frac{-37}{24}\end{array}$

We get wrong answer.