Compute the product of 1/2 ⋅ 5/7

Question

, then use that answer to complete this comparison statement: 1/2 ⋅ 5/7
__ 1/2
. Enter > or < for your response.(1 point)

Answer 1

To compute the product of \( \frac{1}{2} \cdot \frac{5}{7} \):

\[ \frac{1}{2} \cdot \frac{5}{7} = \frac{1 \cdot 5}{2 \cdot 7} = \frac{5}{14} \]

Next, we need to compare \( \frac{5}{14} \) with \( \frac{1}{2} \).

To compare these fractions, we can convert \( \frac{1}{2} \) to a fraction with a denominator of 14:

\[ \frac{1}{2} = \frac{1 \cdot 7}{2 \cdot 7} = \frac{7}{14} \]

Now we compare \( \frac{5}{14} \) and \( \frac{7}{14} \):

Since \( 5 < 7 \), we find that:

\[ \frac{5}{14} < \frac{7}{14} \]

Thus, we can complete the comparison statement:

\[ \frac{1}{2} \cdot \frac{5}{7} < \frac{1}{2} \]

The answer is \( < \).