Simplify 2 1/2×1 4/1+2

To simplify the expression \( 2 \frac{1}{2} \times 1 \frac{4}{1} + 2 \), first convert the mixed numbers to improper fractions.

1. Convert \( 2 \frac{1}{2} \):
\[
2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \quad \text{(improper fraction: } \frac{5}{2}\text{)}
\]

2. Convert \( 1 \frac{4}{1} \):
\[
1 \frac{4}{1} = 1 \times 1 + 4 = 1 + 4 = 5 \quad \text{(improper fraction: } \frac{5}{1}\text{)}
\]

So now the expression becomes:
\[
\frac{5}{2} \times \frac{5}{1} + 2
\]

Next, multiply the fractions:
\[
\frac{5}{2} \times \frac{5}{1} = \frac{5 \times 5}{2 \times 1} = \frac{25}{2}
\]

Now, add \( 2 \) (which can be expressed as \( \frac{2}{1} \)). To add these two fractions, convert \( 2 \) to a fraction that has the same denominator:
- Convert \( 2 \) to \( \frac{4}{2} \) (since \( 2 = \frac{2 \times 2}{1 \times 2} = \frac{4}{2} \)).

Now add:
\[
\frac{25}{2} + \frac{4}{2} = \frac{25 + 4}{2} = \frac{29}{2}
\]

Thus, the final simplified expression is:
\[
\frac{29}{2}
\]

This can also be written as a mixed number:
\[
14 \frac{1}{2}
\]

So, the simplified result is:
\[
\frac{29}{2} \text{ or } 14 \frac{1}{2}
\]