Question

find five rational numbers between 2/5 & 1/4

Answer 1

By Multiplying and Dividing (2/5) by 8. and Multiplying and Dividing (1/4) by 10 we get.

(2/5)=16/40
and (1/4)=10/40

so 5 rational no: between 2/5 and 1/4 are...

11/40. 12/40. 13/40. 14/40. 15/40.

Hope it Helps...

Regards,
Leukonov.

Answer 2

Given: Two rational numbers $\frac{2}{5}$ and $\frac{1}{4}$

To find: Five rational numbers between the given numbers

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

The LCM of their denominators 5 and 4 = 20

To make rational numbers with same denominator, we have

$\frac{2}{5} = \frac{2}{5}$ × $\frac{4}{4} = \frac{8}{20}$ and $\frac{1}{4} = \frac{1}{4}$ × $\frac{5}{5} = \frac{5}{20}$

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

$\frac{8}{20} = \frac{8}{20}$ × $\frac{6}{6} = \frac{48}{120}$ and $\frac{5}{20} = \frac{5}{20}$ × $\frac{6}{6} = \frac{30}{120}$

We know that 31, 32, 33, 34, 35, 36, 37, 38, ...47 are integers between 30 and 48.

We can choose any 5 rational numbers.

Hence, five rational numbers between $\frac{2}{5}$ and $\frac{1}{4}$ are : $\frac{31}{120}, \frac{33}{120}, \frac{40}{120}, \frac{45}{120} \ and \ \frac{47}{120}$