Question

In the​ diagram, StartFraction a Over b EndFraction equals seven ninths
. Complete the statement below. Justify your answer.
b
a
7
9
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Part 1
nothing equals StartFraction b Over 9 EndFraction
  
​(Type the ratio as a simplified​ fraction.)

Answer 1

Given that \(\frac{a}{b} = \frac{7}{9}\), we can rewrite this equation in terms of \(b\). To express \(b\) in terms of \(a\), we can cross-multiply:

\[
9a = 7b
\]

From this, we can solve for \(b\):

\[
b = \frac{9}{7}a
\]

Now, to express the statement "nothing equals \(\frac{b}{9}\)", we can substitute \(b\) with \(\frac{9}{7}a\):

\[
\frac{b}{9} = \frac{\frac{9}{7}a}{9} = \frac{a}{7}
\]

This means:

\[
\frac{a}{7} = \frac{b}{9}
\]

Thus, we can complete the statement as follows:

\[
\frac{b}{9} = \frac{a}{7}
\]

So, to summarize, the relationship between \(b\) and \(a\) based on the initial proportion is:

\[
\frac{b}{9} = \frac{a}{7}
\]

This is the simplified ratio that corresponds to the given proportions.