Question

Insert a rational number between 1/2 and 1/3 by mean method?​

Answer 1

`(5)/(12)`

Explanation:

To find a rational number by the mean method.

Add the 2 fractions and divide the result by 2

`(1)/(2)` +
`(1)/(3)`

To add the fractions we require them to have a common denominator.

The LCM of 2 and 3 is 6 ← required common denominator

Multiply numerator/denominator of first fraction by 3

Multiply numerator/denominator of second fraction by 2

=
`(1(3))/(2(3))` +
`(1(2))/(3(2))`

=
`(3)/(6)` +
`(2)/(6)` ( add numerators, leaving denominator )

=
`(5)/(6)`

Now divide by 2

`(5)/(6)` ÷ 2 leave first, change division to multiplication, turn second upside down )

=
`(5)/(6)` ×
`(1)/(2)`

=
`(5)/(12)`

This is the fraction midway between the 2 given fractions