Question

Enter > or < to make this statement true 5/9 • 10/7 ____ 5/9 • 10/7 blank 5/9

Answer 1

To determine the correct inequality, let's simplify the left-hand side of the original statement.

We have:
\[
\frac{5}{9} \cdot \frac{10}{7}
\]

Calculating that:
\[
= \frac{5 \cdot 10}{9 \cdot 7} = \frac{50}{63}
\]

Now we have the inequality:
\[
\frac{50}{63} \, ? \, \frac{5}{9}
\]

Next, let's express \(\frac{5}{9}\) with a common denominator to compare. The denominator 63 can be used:
\[
\frac{5}{9} = \frac{5 \cdot 7}{9 \cdot 7} = \frac{35}{63}
\]

Now we can compare \(\frac{50}{63}\) and \(\frac{35}{63}\):
\[
\frac{50}{63} \, ? \, \frac{35}{63}
\]

Clearly, \(50 > 35\).

Thus:
\[
\frac{50}{63} > \frac{35}{63}
\]

This means:
\[
\frac{5}{9} \cdot \frac{10}{7} > \frac{5}{9}
\]

The correct answer is:
\[
>
\]

So, the completed statement is:
\[
\frac{5}{9} \cdot \frac{10}{7} \, > \, \frac{5}{9}
\]