Question

In the​ diagram, StartFraction a Over b EndFraction equals five sixths
. Complete the statement below. Justify your answer.
b
a
5
6
Question content area bottom
Part 1
nothing equals StartFraction b Over 6 EndFraction
  
​(Type the ratio as a simplified​ fraction.)

Answer 1

We start with the information that:

\[
\frac{a}{b} = \frac{5}{6}
\]

To find the relationship \( \frac{b}{6} \), we can manipulate the equation. First, we can cross-multiply to express \( a \) in terms of \( b \):

\[
6a = 5b
\]

Now, let's express \( b \) in terms of \( a \):

\[
b = \frac{6a}{5}
\]

Now, we find \( \frac{b}{6} \):

\[
\frac{b}{6} = \frac{\frac{6a}{5}}{6} = \frac{6a}{5 \times 6} = \frac{a}{5}
\]

Thus, it follows that:

\[
\frac{b}{6} = \frac{a}{5}
\]

So, summarizing our answer, we state that:

\[
\frac{a}{5} = \frac{b}{6}
\]

This means that:

\[
\frac{b}{6} = \frac{a}{5}
\]

And therefore the complete statement is:

\[
\frac{b}{6} = \frac{a}{5}
\]

This reflects that \( \frac{b}{6} \) equals \( \frac{a}{5} \) based on our calculations.