Ex.1.1 Q3 Number System Solution - NCERT Maths Class 9

Find five rational numbers between \(\begin{align}\frac{3}{4} \text{ and } \frac{4}{5}\end{align}\)

Text Solution

Steps:

Since we make the denominator same first, then

\[\begin{align} \frac{3}{4} &=\frac{3 \times 5}{4 \times 5} \\ &=\frac{15}{20} \\ \frac{4}{5} &=\frac{4 \times 4}{5 \times 4} \\ &=\frac{16}{20} \end{align}\]

Now, we have to find \(5\) rational numbers.

\[\begin{align}\therefore\,\frac{15}{20}& =\frac{15\times 6}{20\times 6} \\ &=\frac{90}{120} \\ \frac{16}{20} &=\frac{16\times 6}{20\times 6} \\ & =\frac{96}{120} \\ \end{align}\]

\(\therefore\) Five rational numbers between  \(\frac{3}{4}\) and \(\frac{4}{5}\) are

\[\begin{align}\frac{91}{120}, \frac{92}{120}, \frac{93}{120}, \frac{94}{120} \text { and } \frac{95}{120} \end{align}\]