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Find five rational numbers between $\frac{3}{5}$ 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 and dividing them with ($5+1=6$).
$\frac{15}{20}\ \times\ \frac{6}{6}\ =\ \frac{90}{120}$
$\frac{16}{20}\ \times\ \frac{6}{6}\ =\ \frac{96}{120}$
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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