Question

Enter > or < to make this statement true: 5/9⋅10/7
_____ 5/9
.(1 point)

Answer 1

To compare the two fractions \( \frac{5}{9} \cdot \frac{10}{7} \) and \( \frac{5}{9} \), we can simplify the comparison.

Calculating \( \frac{5}{9} \cdot \frac{10}{7} \):

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

Now, we need to compare \( \frac{50}{63} \) with \( \frac{5}{9} \). To do this, we can cross-multiply to avoid dealing directly with fractions:

\[
50 \cdot 9 \quad \text{and} \quad 5 \cdot 63
\]

Calculating these products:

\[
50 \cdot 9 = 450
\]
\[
5 \cdot 63 = 315
\]

Now we compare 450 and 315:

\[
450 > 315
\]

Since \( \frac{50}{63} > \frac{5}{9} \), we can fill in the comparison:

\[
\frac{5}{9} \cdot \frac{10}{7} \quad > \quad \frac{5}{9}
\]

So the answer is:

>