Question

find two rational numbers between 1/2 and 2/3

Answer 1

LCM of 2 and 3 is 6.
1/2=3/6=9/18
2/3=4/6=12/18
10/18,11/18 are 2 rational numbers between 1/2 and 2/3.

Answer 2

Given:

Two fractions 1/2 and 2/3.

To find:

Two rational numbers between the given fractions.

Solution:

As we know that the rational numbers can be written in the form of p/q. So, to find the rational numbers between the given fractions 1/2 and 2/3, we need to make the denominators of both fractions the same.

So, we take the LCM of denominators of given fractions i.e. 2 and 3.

The LCM of 2 and 3 is 6.

So, we multiply 3 and 2 on both denominator and numerator of 1/2 and 2/3 respectively. We have,

$\frac{1 \times 3}{2 \times 3} \: and \: \frac{2 \times 2}{3 \times 2}$

$\frac{3}{6} \: and \: \frac{4}{6}$

But, there is no rational number between 3/6 and 4/6.

So, we multiply 3 on both numerator and denominator of both fractions 3/6 and 4/6 so that we get two rational numbers between them. Hence, we have,

$\frac{3 \times 3}{6 \times 3} \: and \: \frac{4 \times 3}{6 \times 3}$

$\frac{9}{18} \: and \: \frac{12}{18}$

Between 9/18 and 12/18, only two rational numbers are present which is 10/18 and 11/18.

Hence, the two rational numbers between 1/2 and 2/3 are 10/18 and 11/18.