Simplify 1 7/8×2 4/5

To simplify \( 1 \frac{7}{8} \times 2 \frac{4}{5} \), we first convert the mixed numbers into improper fractions.

1. Convert \( 1 \frac{7}{8} \):
\[
1 \frac{7}{8} = 1 \times 8 + 7 = 8 + 7 = \frac{15}{8}
\]

2. Convert \( 2 \frac{4}{5} \):
\[
2 \frac{4}{5} = 2 \times 5 + 4 = 10 + 4 = \frac{14}{5}
\]

Now we multiply the two improper fractions:
\[
\frac{15}{8} \times \frac{14}{5} = \frac{15 \times 14}{8 \times 5}
\]

Calculating the numerators and denominators:
- Numerator: \( 15 \times 14 = 210 \)
- Denominator: \( 8 \times 5 = 40 \)

So we have:
\[
\frac{210}{40}
\]

Next, we simplify \( \frac{210}{40} \). We need to find the greatest common divisor (GCD) of 210 and 40. The GCD is 10.

Now we divide the numerator and denominator by their GCD:
\[
\frac{210 \div 10}{40 \div 10} = \frac{21}{4}
\]

Now we can convert \( \frac{21}{4} \) back to a mixed number:
\[
21 \div 4 = 5 \quad \text{with a remainder of } 1
\]
Thus, \( \frac{21}{4} = 5 \frac{1}{4} \).

The final simplified result is:
\[
\boxed{5 \frac{1}{4}}
\]