Question

find three rational numbers between 2 by 3 and 1 by 4​

Answer 1

Answer

$\frac{2}{3} + \frac{1}{4} \div 2 = \frac{8 + 12}{12} \div 2$

$= \frac{11}{12} \div \frac{11}{12} \times \frac{1}{2} = \frac{11}{24}$

$\frac{2}{3} < \frac{11}{24} < \frac{1}{4}$

Chose:-

$\frac{ - 2}{3} \: and \: \: \frac{11}{24}$

$\frac{2}{3} + \frac{11}{24} \div 2$

$= \frac{16 + 11} {24} \div 2$

$= \frac{27}{24} \div 2$

$= \frac{27}{24} \times \frac{1}{2} = \frac{27}{48}$

$= \frac{2}{3} < \frac{27}{48} < \frac{11}{24} < \frac{1}{4}$

$\frac{11}{24} + \frac{1}{4} \div 2 = \frac{11}{24} + 6 \div 2$

$= \frac{17}{24} \div 2 = \frac{17}{24} \times \frac{1}{2} = \frac{17}{18}$

Therefore,

$\frac{3}{3} < \frac{27}{28} < \frac{11}{24} < \frac{17}{28} < \frac{1}{4}$

Hence solution proved :)

Answer 2

Answer:

1/3, 5/12, 1/2 and 7/12

Step-by-step explanation:

Given rational numbers are 2/3 and 1/4.

The LCM of 3 and 4 is 12.

2/3 = 8/12 and 1/4 = 3/12

Between 3/12 and 8/12, we have 4 rational numbers: 4/12, 5/12, 6/12 and 7/12 or, 1/3, 5/12, 1/2 and 7/12.