Solve Mixed Number Multiplication: 1³/₉ × 2²/4

To solve the problem $1\frac{3}{9} \times 2\frac{2}{4}$, we will follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Multiply the improper fractions.
• Step 3: Convert the resulting improper fraction back into a mixed number.

Let’s begin with each step in detail:

Step 1: Convert $1\frac{3}{9}$ and $2\frac{2}{4}$ to improper fractions.
- For $1\frac{3}{9}$: Convert the fraction $\frac{3}{9}$ to its simplest form, which is $\frac{1}{3}$. Then, the mixed number $1\frac{1}{3}$ becomes $1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}$.
- For $2\frac{2}{4}$: The fraction $\frac{2}{4}$ simplifies to $\frac{1}{2}$. Then, the mixed number $2\frac{1}{2}$ becomes $2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$.

Step 2: Multiply the improper fractions:
$\frac{4}{3} \times \frac{5}{2} = \frac{4 \times 5}{3 \times 2} = \frac{20}{6}$.

Simplify $\frac{20}{6}$:
Find the greatest common divisor (GCD) of 20 and 6, which is 2. Then $\frac{20}{6} = \frac{20 \div 2}{6 \div 2} = \frac{10}{3}$.

Step 3: Convert the improper fraction $\frac{10}{3}$ back to a mixed number:
Divide 10 by 3 to get 3 with a remainder of 1, thus $\frac{10}{3} = 3\frac{1}{3}$.

Therefore, the product is $3\frac{1}{3}$.