Question

Find three rational numbers between (1)/(6) and (1)/(3)

Answer 1

Step 1: Find the LCM of the denominators.

LCM of 3 and 6 is 6.

Step 2: Make the denominators equal.

$\frac{1}{6} = \frac{1}{6}$  

$\frac{1}{3} =\frac{2}{6}$

Step 3: Multiply any number to the numerator and the denominator if there isn't the required number of numbers after finding the LCM. Here I am multiplying 4 but you can multiply any number.

$\frac{1}{6} =\frac{4}{24}$

$\frac{2}{6} = \frac{8}{24}$

Step 4: List the rational numbers.

Rational numbers between $\frac{4}{24}$ and $\frac{8}{24}$ are ⇒ $\frac{5}{24},\frac{6}{24},\frac{7}{24}$

∴ The three rational number between $\frac{4}{24}$ and $\frac{8}{24}$ are $\frac{5}{24},\frac{6}{24},\frac{7}{24}$.