Question

find any five rational numbers between 1/4 and 1/5

Answer 1

1/4 and 1/5
Sol:- take LCM of 4 and 5
So LCM = 20
Substituting 1/4 and1/5 by 20
1/4*5 and 1/5*4
= 5/20 and 4/20

Now multiply 5/20 and 4/20 by 5
= 5/20*10 and 4/20*10
= 50/200 and 40/200
The five rational numbers between 1/4 and1/5 are 41/200, 42/200, 43/200, 44/200, 45/200


Hope this helps u

Answer 2

Given: Two rational numbers $\frac{1}{4}$ and $\frac{1}{5}$

To find: Five rational numbers between the given numbers

Solution: The given numbers have different denominators. First we need to make their denominators same.

LCM of their denominators 4 and 5 = 20

To convert these rational numbers with same denominators, we have

$\frac{1}{4} = \frac{1}{4}$ × $\frac{5}{5} = \frac{5}{20}$ and $\frac{1}{5} = \frac{1}{5}$ × $\frac{4}{4} = \frac{4}{20}$

To insert five rational numbers, multiply both the numerator and denominator of each rational number by 5 + 1 i.e., 6

We have, $\frac{5}{20} = \frac{5}{20}$ × $\frac{6}{6} = \frac{30}{120}$ and $\frac{4}{20} = \frac{4}{20}$ × $\frac{6}{6} = \frac{24}{120}$

∵ $24 < 25 < 26 < 27 < 28 < 29 < 30$

∴ $\frac{24}{120} < \frac{25}{120} < \frac{26}{120} < \frac{27}{120} < \frac{28}{120} < \frac{29}{120} < \frac{30}{120}$

Hence, 5 rational numbers between $\frac{1}{4}$ and $\frac{1}{5}$ are:

$\frac{25}{120}, \frac{26}{120}, \frac{27}{120}, \frac{28}{120} \ and \ \frac{29}{120}$.