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

1 Answer

  • 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