Question

How do you find a fraction between 1/5 and 1/4?

Answer 1

Find the mean of the two numbers

`(1/5+1/4)/2=(9/20)/(2/1)=(9*1)/(20*2)=9/40`

this is always halfway between the two numbers

Answer 2

Convert to equivalent fractions with a common denominator and then choose a suitable numerator between the ones you have calculated..

Explanation:

Change to a common denominator.
`1/5 and 1/4` can be changed to `4/20 and 5/20`

However, the only values between 4 and 5 are fractions.
for example: `4.5/20 = 9/40`
This would require further simplifying.

Use a different common denominator: `8/40 and 10/40`
`9/40`is between them.

Similarly for any common denominator with a value higher than 40:

`12/60 and 15/60` or `16/80 and 20/80`

The question does not ask for a fraction midway between them, so any of the following would be possible answers:

`13/60 , 14/60 , 17/80, 18/80 , 19/80`etc.

Answer 3

See below.

Explanation:

If you have two numbers `lambda_1 < lambda_2`

then you have infinite numbers in between them. You can construct them as

`mu = lambda_1 +eta(lambda_2-lambda_1)` or
`mu = eta lambda_1 + (1 - eta)lambda_2`

with `0 < eta < 1` so

`lambda_1 < mu < lambda_2`

Example: choosing `eta = 3/5`

`1/5 < 3/5xx1/5+(1-3/5)xx1/4 < 1/4` or

`1/5 < 11/50 < 1/4`