Calculate Rectangle Area: 2½ m × 3¼ m Mixed Number Multiplication

To find the area of a rectangle when given the dimensions as mixed numbers, follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Multiply the two fractions to find the area.
• Step 3: Simplify the resulting fraction, if necessary, back to a mixed number.

Step 1: Convert the mixed numbers to improper fractions.

The length is $2\frac{1}{2}$ meters. To convert $2\frac{1}{2}$ to an improper fraction:

• Multiply the whole number (2) by the denominator of the fractional part (2): $2 \times 2 = 4$.
• Add this result to the numerator of the fractional part (1): $4 + 1 = 5$.
• The improper fraction is $\frac{5}{2}$.

The width is $3\frac{1}{4}$ meters. To convert $3\frac{1}{4}$ to an improper fraction:

• Multiply the whole number (3) by the denominator of the fractional part (4): $3 \times 4 = 12$.
• Add this result to the numerator of the fractional part (1): $12 + 1 = 13$.
• The improper fraction is $\frac{13}{4}$.

Step 2: Multiply the two improper fractions.

$\text{Area} = \frac{5}{2} \times \frac{13}{4} = \frac{5 \times 13}{2 \times 4} = \frac{65}{8}$.

Step 3: Simplify $\frac{65}{8}$ to a mixed number.

• The quotient of $65 \div 8$ gives 8 as the whole number.
• The remainder is $65 - (8 \times 8) = 65 - 64 = 1$.
• Thus, $\frac{65}{8}$ converts to the mixed number $8\frac{1}{8}$.

Therefore, the area of the rectangle is $\mathbf{8\frac{1}{8}}$ m².