Chapter 3.6, Problem 52HP

To determine

Toexplain whether using the common denominator as 24 instead of 12 will conclude the correct answer.

Answer to Problem 52HP

The solution of the fractions using the common denominator as 24 instead of 12 is, $-3\frac{1}{12}$ , that is correct.

Explanation of Solution

Given information :

The fraction is given as, $2\frac{3}{4}-5\frac{5}{6}$ and the common denominator is said to use 24 instead of 12.

The common denominator must be such an integer that can be divided by the given denominators. As for 24 can be divided by the denominators of the given fractions, the answer that can be obtained must be correct.

The solution of the fractions using the common denominator as 24 instead of 12 can be obtained as,

  $\begin{array}{l}2\frac{3}{4}-5\frac{5}{6}\\ =\frac{11}{4}-\frac{35}{6}\\ =\frac{11}{4}\cdot \frac{6}{6}-\frac{35}{6}\cdot \frac{4}{4}\left[\text{use 24 as the common denominator}\right]\\ =\frac{66}{24}-\frac{140}{24}\left[\text{write the fraction using common denominator}\right]\\ =-\frac{74}{24}\left[\text{subtract the numerator}\right]\\ =-3\frac{1}{12}\left[\text{simplify}\right]\end{array}$

Therefore,

The solution of the fractions using the common denominator as 24 instead of 12 is, $-3\frac{1}{12}$ , that is correct.