How can we find ten rational numbers between $\frac{3}{5} \ and \ \frac{ 4}{15}$?


To do:  Find Ten Rational Numbers between $\frac{3}{5} \ and \ \frac{ 4}{15}$?

Solution:

$\frac{3}{5} \ and \ \frac{ 4}{15}$

LCM of denominators is 15.

To convert into like fractions we will multiply numerator and denominator of $\frac{3}{5}$ with 3.

$\frac{3}{ 5} = \frac{3\times3}{5\times3} = \frac{9}{15}$.

Now our numbers are $\frac{4}{15}$ and $\frac{9}{15}$.

Now in between the numerators 4 and 9, there are 4 numbers. 

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

Let us multiply both the numbers numerator and denominator with 3.

$\frac{4}{15} \times \frac{3}{3} =  \frac{12}{45}$

$\frac{9}{15}\times{3}{3} =  \frac{27}{45}$

So, the two numbers are $\frac{12}{45} and \frac{27}{45}$.

Now we find Ten Rational Numbers between them as:


 $\frac{13}{45}, \frac{14}{45},\frac{15}{45},\frac{16}{45},\frac{17}{45},\frac{18}{45},\frac{19}{45},\frac{20}{45},\frac{21}{45},\frac{22}{45}$


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Updated on: 10-Oct-2022

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