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Find five rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$.
Given:
$\frac{3}{5}$ and $\frac{3}{4}$
To find:
We need to find 5 rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$.
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 $\frac{3}{5}$ with 4.
$\frac{3}{5} \ =\ \frac{3}{5}\ \times\ \frac{4}{4}\ =\ \frac{12}{20}$
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 $\frac{12}{20}$ and $\frac{15}{20}$.
We can find 5 rational numbers between $\frac{12}{20}$ and $\frac{15}{20}$ by multiplying them with ($5+1=6$).
$\frac{12}{20}\ \times\ \frac{6}{6}\ =\ \frac{72}{120}$
And,
$\frac{15}{20}\ \times\ \frac{6}{6}\ =\ \frac{90}{120}$
Therefore,
Five rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$ are:
$\frac{73}{120},\ \frac{74}{120},\ \frac{75}{120},\ \frac{76}{120}\ and\ \frac{77}{120}$.
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