Question

find five rational numbers between 5/4 and 2

Answer 1

Answer:

17/16 and 19/16

Answer 2

Given: Two rational numbers $\frac{5}{4}$ and 2

To find: Five rational numbers between the given numbers

Solution:

Given rational numbers are  $\frac{5}{4}$ and 2.

Using mean method :

To insert rational numbers between the given numbers, we need to find the mean of  $\frac{5}{4}$ and 2.

i.e., $(\frac{5}{4} + 2 )$ ÷ $2 = (\frac{5 \ + \ 8}{4} )$ ÷ $2 = \frac{13}{4}$ ÷ $2 = \frac{13}{4} * \frac{1}{2} = \frac{13}{8}$

We get,  $\frac{5}{4} < \frac{13}{8} < 2$

We now need to find another rational number between $\frac{5}{4} \ and \ \frac{13}{8}$

i.e., $(\frac{5}{4} + \frac{13}{8})$ ÷ $2 = (\frac{10 \ + \ 13}{8})$ ÷ $2 = \frac{23}{8}$ ÷ $2 = \frac{23}{8} * \frac{1}{2} = \frac{23}{16}$

We get, $\frac{5}{4} < \frac{23}{16} < \frac{13}{8} < 2$

We now need to find another rational number between $\frac{13}{8} \ and \ 2$

i.e., $(\frac{13}{8} + 2)$ ÷ $2 = (\frac{13 \ + \ 16}{8} )$ ÷ $2 = \frac{29}{8} * \frac{1}{2} = \frac{29}{16}$

We get, $\frac{5}{4} < \frac{23}{16} < \frac{13}{8} < \frac{29}{16} < 2$

Similarly, we find rational numbers between $\frac{13}{8} \ and \ \frac{23}{16} \ , \ \frac{13}{8} \ and \ \frac{29}{16}$, we get $\frac{49}{32} \ and \ \frac{55}{32}$ respectively.

Hence, five rational numbers between the given numbers are:

$\frac{23}{16}, \frac{49}{32}, \frac{13}{8}, \frac{55}{32} \ and \ \frac{29}{16}$