Question

find five rational numbers between 1/8 and 1/5 ​

Answer 1

16/120,17/120,19/120,18/120,20/120 this u r answer

Answer 2

Given:

• Rational numbers between $\sf\dfrac{1}{8}$ and $\sf\dfrac{1}{5}$

To Find:

• Find five rational numbers = ?

Solution:

According to the question,we are said to find five rational numbers between 1/8 and 1/5.

So as we know that,

$\: \: \sf \: difference = \frac{greater - smaller}{n + 1}$

Now put values here to find the answer

$\: \: \sf \: d = \frac{y - x}{n + 1}$

$\: \: \sf \: d = \frac{ \frac{1}{5} - \frac{1}{8} }{5 + 1} \\ \\ \: \: \sf \: d = \frac{ \frac{3}{40} }{6} \\ \\ \: \: \sf \: d = \frac{3}{40} \times 6 \\ \\ \: \: \sf \: d = \frac{9}{20}$

Hence, difference is 9/20.

Now find rational numbers

$\: \: \sf \: 1st \: rational \: no. = x + d \\ \\ \: \: \: \: \: \: \sf = ( \frac{1}{8} + \frac{9}{20} ) \\ \\ \: \: \: \: \: \sf \: = \frac{23}{40}$

$\: \: \sf \: 2nd \: rational \: no. = x + 2d \\ \\ \: \: \: \: \: \: \sf \: = \frac{23}{40} + \frac{9}{20} \\ \\ \: \: \: \: \: \: \sf \: = \frac{41}{40}$

$\: \: \sf \: 3rd \: rational \: no. = x + 3d \\ \\ \: \: \: \: \: \: \sf \: = \frac{41}{40} + \frac{9}{20} \\ \\ \: \: \: \sf \: = \frac{59}{40}$

$\: \: \sf \: 4th \: rational \: no. = x + 4d \\ \\ \: \: \: \: \: \: \: \sf \: = \frac{59}{40} + \frac{9}{20} \\ \\ \: \: \: \: \: \sf \: = \frac{77}{40}$

$\: \: \sf \: 5th \: rational \: no. = x + 5d \\ \\ \: \: \: \: \: \sf \: = \frac{77}{40} + \frac{9}{20} \\ \\ \: \: \: \: \: \sf \: = \frac{95}{40}$

Hence, five rational numbers are 23/40,41/40,59/40,77/40 and 95/40.

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