The problem asks for the value of the expression:

$t \times 2 \frac{1}{2}$

where $t = 2 \frac{2}{7}$.

Steps:

1. Convert the mixed numbers to improper fractions:

   • $2 \frac{1}{2} = \frac{5}{2}$
   • $2 \frac{2}{7} = \frac{16}{7}$

2. Substitute the value of $t$:

   • Now, the expression becomes: $\frac{16}{7} \times \frac{5}{2}$

3. Multiply the fractions: $\frac{16 \times 5}{7 \times 2} = \frac{80}{14}$

4. Simplify the fraction: $\frac{80}{14} = \frac{40}{7}$

So, the value of the expression is $\frac{40}{7}$, which is also $5 \frac{5}{7}$ as a mixed number.

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you convert a mixed number into an improper fraction?
2. What is the process for multiplying two fractions?
3. How can you simplify fractions?
4. What is the difference between a proper and improper fraction?
5. Can you explain how to convert an improper fraction back into a mixed number?

Tip: When multiplying fractions, you multiply the numerators together and the denominators together, then simplify if possible!