Question

Enter > or < to make this statement true: 6/5⋅9/2
__ 6/5
.

Answer 1

To determine the relationship between \( \frac{6}{5} \cdot \frac{9}{2} \) and \( \frac{6}{5} \), we first need to calculate \( \frac{6}{5} \cdot \frac{9}{2} \).

Calculating:

\[
\frac{6}{5} \cdot \frac{9}{2} = \frac{6 \cdot 9}{5 \cdot 2} = \frac{54}{10} = \frac{27}{5}
\]

Now, we need to compare \( \frac{27}{5} \) and \( \frac{6}{5} \):

Since both fractions are over the same denominator of 5, we can compare the numerators directly:

\[
27 \quad \text{and} \quad 6
\]

Clearly, \( 27 > 6 \).

Thus,

\[
\frac{27}{5} > \frac{6}{5}
\]

So the correct symbol is:

\[
\frac{6}{5} \cdot \frac{9}{2} \, > \, \frac{6}{5}
\]

The final statement is:

\[
>
\]