Solve Mixed Number Multiplication: 2 10/20 × 1 4/16

To solve this problem, we will convert the mixed numbers to improper fractions and multiply them.

• Step 1: Convert Mixed Numbers to Improper Fractions

For the first mixed number $2\frac{10}{20}$:
- Convert $2\frac{10}{20}$ to an improper fraction:
Initially, $10/20$ can be simplified to $1/2$ (since $\gcd(10, 20) = 10$). Therefore, the mixed number $2\frac{1}{2}$ is equal to:
$2 \times 2 + 1 = 4 + 1 = 5$
Thus, $2\frac{1}{2}$ becomes $\frac{5}{2}$.

For the second mixed number $1\frac{4}{16}$:
- Simplify $4/16$ to $1/4$ (since $\gcd(4, 16) = 4$). Hence, $1\frac{4}{16}$ simplifies to $1\frac{1}{4}$:
$1 \times 4 + 1 = 4 + 1 = 5$
Thus, $1\frac{1}{4}$ becomes $\frac{5}{4}$.

• Step 2: Multiply the Improper Fractions

Multiply the fractions $\frac{5}{2} \times \frac{5}{4}$:
$\frac{5 \times 5}{2 \times 4} = \frac{25}{8}$

• Step 3: Simplify and Convert to Mixed Number

Convert $\frac{25}{8}$ back to a mixed number by dividing:
- Divide 25 by 8, which goes 3 times (remainder 1).
Thus, $\frac{25}{8} = 3\frac{1}{8}$.

Therefore, the solution to the problem is $3\frac{1}{8}$.