DAY 08

Comment

One approach is to change the fractions to equivalent fractions, for example 1/4 is the same as 2/8 and 1/5 is the same as 2/10. Or change the fractions to decimals (eg by using a calculator), find an intermediate decimal and change it back to a vulgar fraction.

Answer

eg, 2/9.
[This is perhaps the most obvious fraction between 1/4 and 1/5, but of course there are countless others: eg, 24/100, 23/100, ....]

Readers' methods

Julian P, Darlington DL3:
1/4 = 10/40, 1/5 = 8/40,
so an answer is 9/40.

Sue B, Bristol BS35:
Convert both to twentieths:
5/20 and 4/20.
Because there is not a whole number between 5 and 4, convert these two fractions to fortieths:
10/40 and 8/40.
9/40 is between these two, so is a solution.

Frances P, London NW3:
1/4 and 1/5 is the same as 2/8 and 2/10,
therefore 2/9 is between the two.

Mark B, Helston TR12:
1/4.5 = 2/9.

Anne H, Runcorn WA7:
Change to fractions with the same denominator, for example
5/20, 4/20.
Somewhere between would be 4 1/2 / 20,
which must be written 9/40.

Anne N, Worthing BN14:
eg, 1/4 = 3/12 and 1/5 = 3/15.
Gaps between 3/12 and 3/15 are 3/13 and 3/14.
Or, for example, gaps between 4/16 and 4/20 are 4/17, 4/18 (2/9) and 4/19.
And so on.

Tom Crispin:
A general solution to finding a fraction between a/b and c/d is (a+c) / (b+d),
so an answer is 2/9.

Harlan Messinger:
1/2 x (1/4 + 1/5) = 1/2 x (10/40 + 8/40)
= 1/2 x 18/40 = 9/40.
More generally, p(1/4) + (1 - p)(1/5) will be between 1/4 and 1/5 for any p between 0 and 1.
Even more generally, px + (1 - p)y will be between x and y for any p between 0 and 1.

Richard P, Poulton le Fylde FY6:
eg 2/9, as
1/4=2/8
1/4.5=2/9
1/5=2/10.