Question

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

• A. $\frac{13}{2}$
• B. $\frac{15}{2}$
• C. $\frac{17}{2}$
• D. $8$

Answer 1

The correct option is A $\frac{13}{2}$

Rational numbers can be compared by making their denominators equal.

Here, we need to compare all given rational numbers $\frac{25}{4},\frac{22}{3},\frac{13}{2},\frac{15}{2},\frac{17}{2}$ and $\frac{8}{1}$.

We know LCM of 1, 2, 3 and 4, i.e., the denominators of the above fractions, is 12.

Converting all the above fractions into like fractions, we get

$\frac{25}{4}=\frac{25\times 3}{4\times 3}=\frac{75}{12}$

$\frac{22}{3}=\frac{22\times 4}{3\times 4}=\frac{88}{12}$

$\frac{13}{2}=\frac{13\times 6}{2\times 6}=\frac{78}{12}$

$\frac{15}{2}=\frac{15\times 6}{2\times 6}=\frac{90}{12}$

$\frac{17}{2}=\frac{17\times 6}{2\times 6}=\frac{102}{12}$

$8=\frac{8}{1}=\frac{8\times 12}{1\times 12}=\frac{96}{12}$

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

Thus, $\frac{13}{2}$ lies between $\frac{25}{4}$ and $\frac{22}{3}$.