Question

Which of the following rational numbers lie between $\frac{25}{4}$ and $\frac{22}{3}$?

• A. Whole number
• B. Irrational number
• C. Non integers
• D. Integers

Answer 1

The correct option is A

Whole number

Rational numbers can be compared by making their denominators equal.
We have the following fractions - $\frac{22}{3},\frac{25}{4},\frac{15}{2},\frac{17}{2},\frac{13}{2}$ and the integer $8$ which can be written as $\frac{8}{1}$
LCM of 1, 2, 3 and 4, i.e., the denominators of the above fractions is 12.
Converting all the fractions above into fractions with a common denominator, we get:
$\frac{22}{3}=\frac{22\times 4}{3\times 4}=\frac{88}{12}$
$\frac{25}{4}=\frac{25\times 3}{4\times 3}=\frac{75}{12}$
$\frac{13}{2}=\frac{13\times 6}{2\times 6}=\frac{78}{12}$
$\frac{15}{2}=\frac{15\times 6}{2\times 6}=\frac{90}{12}$
$\frac{17}{2}=\frac{17\times 6}{2\times 6}=\frac{102}{12}$
$8=\frac{8}{1}=\frac{8\times 12}{1\times 12}=\frac{96}{12}$

Arranging these fractions in an ascending order, we get
$\frac{75}{12},\frac{78}{12},\frac{88}{12},\frac{90}{12},\frac{96}{12},\frac{102}{12}$

Thus, the number between $\frac{22}{3}$ and $\frac{25}{4}$ is $\frac{78}{12}$, i.e. $\frac{13}{2}$