How to insert 7 rational numbers between $\frac{5}{7}$ and $\frac{6}{7}$.

Given:  Two rational numbers$\frac{5}{7}$ and $\frac{6}{7}$.

To do:  Find how to insert 7 between the given numbers

Solution:

To solve this question, first we need to convert them into like fractions.

The given fractions are already like fractions. So we need not adjust

Now in between the numerators 5 and 6, there are no integers. 

So we have to multiply both the numbers numerator and denominator to see that there are sufficient numbers.

Let us multiply both the numbers numerator and denominator with 8.

$\frac{5}{7} \times \frac{8}{8} =  \frac{40}{56}$

$\frac{6}{7} \times \frac{8}{8} = \frac{48}{56}$

So the two numbers are $\frac{40}{56} \ and \ \frac{48}{56}$.

Now we find can Rational Numbers between them that is:
 $\frac{41}{56}$, $\frac{42}{56}, \frac{43}{56}, \frac{44}{56}, \frac{45}{56}, \frac{46}{56}$ and $\frac{47}{56}$

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Updated on: 10-Oct-2022

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