Which of the following lies between 25 4 and 22 3 ? Options: A . &nbsp132 B . &nbsp152 C . &nbsp172 D . &nbsp8

Which of the following lies between 254 and 223?

Question

Which of the following lies between

\frac{25}{4}

and

\frac{22}{3} ?

Options:

A . 132

B . 152

C . 172

D . 8

Answer: Option A
:
A
Rational numbers can be compared by making their denominators equal.
Here,we need to compare allgiven 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}

liesbetween

\frac{25}{4}

and

\frac{22}{3}

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