Question

find a rational number between _2/3 and 1/4

Answer 1

we have 2/3 and 1/4

now multiply 2/3 by 4

2/3 × 4/4 = 8/12

and multiply 1/4 by 3

1/4 × 3/3 = 3/12

The rational no between 2/3 and 1/4 are 4/12 , 5/12 , 6/12 , 7/12 ..

Answer 2

Given: Two rational numbers $\frac{2}{3}$ and $\frac{1}{4}$

To find: A rational number between the given numbers

Solution:

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

LCM of their denominators 3 and 4 = 12

To convert the rational numbers with same denominators, we have

$\frac{2}{3} = \frac{2}{3}$ × $\frac{4}{4} = \frac{8}{12}$ and $\frac{1}{4} = \frac{1}{4}$ × $\frac{3}{3} = \frac{3}{12}$

We see that 4, 5, 6 and 7 are four integers between 3 and 8.

i.e., $\frac{3}{12} < \frac{4}{12} < \frac{5}{12} < \frac{6}{12} < \frac{7}{12} < \frac{8}{12}$

We can choose any one rational number

Hence, $\frac{5}{12}$ is a rational number between $\frac{2}{3} \ and \ \frac{1}{4}$.