Calculate the Product: 2¼ × 1⅔ Mixed Number Multiplication

To solve the problem of multiplying the mixed numbers $2\frac{1}{4}$ and $1\frac{2}{3}$, we proceed as follows:

• Step 1: Convert Mixed Numbers to Improper Fractions

  • Convert $2\frac{1}{4}$ to an improper fraction: $2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$

  • Convert $1\frac{2}{3}$ to an improper fraction: $1\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}$

• Step 2: Multiply the Improper Fractions

• Now, multiply $\frac{9}{4}$ by $\frac{5}{3}$: $\frac{9}{4} \times \frac{5}{3} = \frac{9 \times 5}{4 \times 3} = \frac{45}{12}$

• Step 3: Simplify the Fraction

• Simplify $\frac{45}{12}$ by finding the greatest common divisor of 45 and 12, which is 3: $\frac{45 \div 3}{12 \div 3} = \frac{15}{4}$

• Step 4: Convert Back to a Mixed Number

• Convert $\frac{15}{4}$ into a mixed number: $15 \div 4 = 3 \quad \text{remainder} \quad 3$ So, $\frac{15}{4} = 3\frac{3}{4}$.

Based on the calculations, the product of $2\frac{1}{4}$ and $1\frac{2}{3}$ is $3\frac{3}{4}$.

Therefore, the solution to the problem is $3\frac{3}{4}$.