Question

six rational numbers between 1 and 2​

Answer 1

HOPE THIS HELPS

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Answer 2

Given: Two numbers 1 and 2

To find: Six rational numbers between the given numbers

Solution:

Using average method:

To insert rational numbers between 1 and 2, we need to find the average of  1 and 2.

i.e., $\frac{(1 \ + \ 2)}{2} = \frac{3}{2}$

We get, $1 < \frac{3}{2} < 2$

Now we need to find another rational number between 1 and  $\frac{3}{2}$.

i.e., $(1 \ + \ \frac{3}{2})$ ÷ $2 = \frac{5}{2} \ * \ \frac{1}{2} = \frac{5}{4}$

We get,  $1 < \frac{5}{4} < \frac{3}{2} < 2$

Now we need to find another rational number between $\frac{3}{2}$ and 2.

i.e., $(\frac{3}{2} \ + \ 2)$ ÷ $2 = \frac{7}{2} \ * \ \frac{1}{2} = \frac{7}{4}$

We get, $1 < \frac{5}{4} < \frac{3}{2} < \frac{7}{4} < 2$

Similarly, we find rational numbers between $1 \ and \ \frac{5}{4}, \frac{5}{4} \ and \ \frac{3}{2}, \frac{7}{4} \ and \ 2$. We get, $\frac{9}{8}, \frac{11}{8} \ and \ \frac{15}{8}$ respectively.

i.e., $1 < \frac{9}{8} < \frac{5}{4} < \frac{11}{8} < \frac{3}{2} < \frac{7}{4} < \frac{15}{8} < 2$

Hence, six rational numbers between 1 and 2 are:

$\frac{9}{8}, \frac{5}{4}, \frac{11}{8}, \frac{3}{2}, \frac{7}{4} \ and \ \frac{15}{8}$