Chapter 8.3, Problem 50E

To determine

To choose: the correct option for the given statement.

Answer to Problem 50E

E. Cannot be determined from the given information.

Explanation of Solution

Given information:

The result obtained after adding a same positive quantity to the numerator and the denominator of the fraction is ______.

The options are as follows:

1. Greater than the original faction.
2. Less than the original faction.
3. Equal to the original faction.
4. One half the original fraction
5. Cannot be determined from the given information.

Calculation:

Let the original fraction be $\frac{x}{y}$ and the new fraction obtained after adding a positive number (let’s say 1) is $\frac{x+1}{y+1}$ .

Case I: Substitute $x=2\text{ and }y=3$ in both the fraction and solve as shown below.

  $\begin{array}{c}\text{Original fraction}=\frac{2}{3}\\ =0.6\overline{6}\\ \text{New fraction}=\frac{2+1}{3+1}\\ =\frac{3}{4}\\ =0.75\end{array}$

If $x<y$ then the new fraction will be greater than the original fraction.

Case II: Substitute $x=3\text{ and }y=2$ in both the fraction and solve as shown below.

  $\begin{array}{c}\text{Original fraction}=\frac{3}{2}\\ =1.5\\ \text{New fraction}=\frac{3+1}{2+1}\\ =\frac{4}{3}\\ =1.33\end{array}$

If $x>y$ then the new fraction will be smaller than the original fraction.

Thus the option E. is correct because the answer cannot be determined from the given information.