Find five rational numbers between $\frac{3}{4}$ and $\frac{4}{5}$.


Given: 

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

To find: 

We need to find 5 rational numbers between $\frac{3}{4}$ and $\frac{4}{5}$.

Solution: 

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

LCM of denominators (4 and 5) is 20. Now we have to change the fractions in such a way that denominators become 20.

To convert into like fractions we will multiply the numerator and denominator of $\frac{4}{5}$ with 4.

$\frac{4}{5} \ =\ \frac{4}{5}\ \times\ \frac{4}{4}\ =\ \frac{16}{20}$

We will multiply the numerator and denominator of $\frac{3}{4}$ with 5.

$\frac{3}{4}\ =\ \frac{3}{4}\ \times\ \frac{5}{5}\ =\ \frac{15}{20}$

Now, our numbers are $\frac{15}{20}$ and $\frac{16}{20}$.

There are no integers between 15 and 16.We can find 5 rational numbers between $\frac{15}{20}$ and $\frac{16}{20}$ by multiplying them with ($5+1=6$).

$\frac{15}{20}\ \times\ \frac{6}{6}\ =\ \frac{90}{120}$

And,

$\frac{16}{20}\ \times\ \frac{6}{6}\ =\ \frac{96}{120}$

Five rational numbers between $\frac{3}{4}$ and $\frac{4}{5}$ are: 

$\frac{91}{120},\ \frac{92}{120},\ \frac{93}{120},\ \frac{94}{120}\ and\ \frac{95}{120}$.

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Updated on: 10-Oct-2022

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