Find a fraction between 2/3 and 3/4 with a number of 17?

Answer 1

If you think what is half between 2 / 3 and 3 / 4

Then:

Half the distance between these 2 points:

[ 3 / 4 - 2 / 3 ] / 2 =

[ 3 ∙ 3 / 4 ∙ 3 - 2 ∙ 4 / 3 ∙ 4 ] / 2 =

( 9 / 12 - 8 / 12 ) / 2 =

( 1 / 12 ) / 2 = 1 / 2 ∙ 12 = 1 / 24

1 / 24 is half the distance between these 2 points

Now:

3 / 4 - 1 / 24 = 3 ∙ 6 / 4 ∙ 6 - 1 / 24 =

18 / 24 - 1 / 24 = 17 / 24

OR

2 / 3 + 1 / 24 = 2 ∙ 8 / 3 ∙ 8 + 1 / 24 =

16 / 24 + 1 / 24 = 17 / 24