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Explanation:

you did not include the shown numbers to pick from.

so, I can give you my own examples, but since I don't see your examples, I can't identify any non-fitting or out-of-context number.

berween 2/7 and 2/3 are for example

2/4, 2/5, 2/6

to give you more background, let's compare 2/7 and 2/3 by bringing them to the same denominator (bottom number).

the common denominator is the LCM (least common multiple) of the 2 original numbers (7, 3).

for such small numbers we don't need a formal approach. we can just find the smallest number that is divisible by 7 and 3.

so, let's go with multiples of 7.

is 7 divisible by 3 ? no.

is 14 divisible by 3 ? no

is 21 divisible by 3 ? yes.

so, 21 is the common denominator :

2/7 must be multiplied by 3/3 to get it to .../21 :

2/7 × 3/3 = 2×3 / (7×3) = 6/21

2/3 must be multiplied by 7/7 to get it to .../21 :

2/3 × 7/7 = 2×7 /(3×7) = 14/21

now we see even more fractions between 2/7 and 2/3 :

the fractions between

6/21 and 14/21 are directly

7/21, 8/21, 9/21, 10/21, 11/21, 12/21, 13/21

plus the previously found fractions

2/4 = 1/2, 2/5, 2/6 = 1/3

now every fraction that is between e.g. 2/5 and 2/6 is also between 2/7 and 2/3. or every fraction between 10/21 and 11/21. and so on.

that would be between

10/30 and 12/30 : e.g. 11/30

or between

20/42 and 22/42 : e.g. 21/42 = 1/2 (so, here we hit by pure chance on a number we had already found; that will happen more and more often the more detailed we go into the intervals).

of course, at the end, there are infinitely many fractions (rational numbers) between 2/7 and 2/3.

as between any other pair of numbers (except for identical numbers, of course) .

User Yqritc
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