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

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Answer 1 · 2015-09-16T20:03:01

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 · 2016-05-12T20:53:22

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

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 · 2016-09-25T15:55:13

See below.

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

$1/5 < 11/50 < 1/4$