Question

Find 10 rational numbers between 3/5 and 3/4

Answer 1

The 10 rational numbers are : 121/200, 122/200..........till 130/200

Answer 2

The ten rational numbers are $\frac{49}{80} \frac{50}{80} \frac{51}{80} \frac{52}{80} \frac{53}{80} \frac{54}{80} \frac{55}{80} \frac{56}{80} \frac{57}{80} \frac{58}{80}$

To find:

Rational numbers between $\frac{3}{5} \text { and } \frac{3}{4}$

Step-by-step explanation:

First rationalize $\frac{3}{5}$ by multiplying 4 on both numerator and denominator that will be $\frac{3 \times 4}{5 \times 4}=\frac{12}{20}$

After this rationalize $\frac{3}{4}$ by multiplying 5 on both numerator and denominator that will be $\frac{3 \times 5}{4 \times 5}=\frac{15}{20}$

We now find the number of terms that lies between $\frac{12}{20} \text { and } \frac{15}{20}$, although we can find multiple terms but to find easy terms without complicating and lengthen the process we again rationalize the number $\frac{12}{20} \text { and } \frac{15}{20}$, like before.

Now rationalize $\frac{12}{20}$ by multiplying 4 on both numerator and denominator that will be $\frac{12 \times 4}{20 \times 4}=\frac{48}{80}$

After this rationalize $\frac{15}{20}$ by multiplying 4 on both numerator and denominator that will be $\frac{15 \times 4}{20 \times 4}=\frac{60}{80}$

Now as we can see the term are $\frac{48}{80} \text { and } \frac{60}{80}$, so in between 48 and 60 there are 11 terms so the ten terms will be $\frac{49}{80} \frac{50}{80} \frac{51}{80} \frac{52}{80} \frac{53}{80} \frac{54}{80} \frac{55}{80} \frac{56}{80} \frac{57}{80} \frac{58}{80}$.