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
[tex]\bf \begin{cases}
\cfrac{6}{7}\cdot \cfrac{6}{6}\implies \cfrac{6\cdot 6}{7\cdot 6}\implies \cfrac{36}{42}
\\ \quad \\
\cfrac{5}{6}\cdot \cfrac{7}{7}\implies \cfrac{5\cdot 7}{6\cdot 7}\implies \cfrac{35}{42}
\end{cases}
\\ \quad \\
\textit{so.. hmmm they're next to one another, kinda}\\\\
\textit{let us use }\frac{35}{42}+0.5\textit{ or half a bit more}\\\\
\textit{pass 35 and below 36}
\\ \quad \\
\cfrac{35}{42}+0.5\implies \cfrac{35}{42}+\cfrac{1}{2}[/tex]
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
