What is a rational number halfway between 6/7 and 5/6

Well hmmm let's see hmm
our denominators are 7 and 6

so.. their LCD or a GCF for that matter..  is just 7 * 6 or 42

so let's make both fractons the same denominator,
that is, the LCD of 42

for the 7, we need to multiply by 6
we do that to the denominator, we have to
also do it for its numerator

for the 6, we multiply by 7
we do that for the denominator, we need to
also do it for its numerator

so, we end up with 


so.. that rational is, passed 35/42 and  before 36/42
so. is between, half-way really, since we used 1/2

now, we could have use some other fraction of 1,
say 1/25 or 1/7 or 3/23  and those would have also worked,
because they're passed 35/42 and before 36/42

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