Calculate Rectangle Area: 4 2/3 by 2 1/4 Meters

To solve this problem, we'll proceed as follows:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Multiply the fractions to find the area.
• Step 3: Convert the result back to a mixed number, if applicable.

Let's work through these steps:

Step 1: First, convert the mixed numbers to improper fractions.

The length is $4\frac{2}{3}$ meters. Convert this to an improper fraction: $4\frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}$

The width is $2\frac{1}{4}$ meters. Convert this to an improper fraction: $2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$

Step 2: Multiply these improper fractions to find the area.

Thus, the area $A$ of the rectangle in square meters is: $A = \frac{14}{3} \times \frac{9}{4} = \frac{14 \times 9}{3 \times 4} = \frac{126}{12}$

Simplify the fraction $\frac{126}{12}$:

Both the numerator and the denominator can be divided by 6: $\frac{126 \div 6}{12 \div 6} = \frac{21}{2}$

Step 3: Convert the improper fraction back to a mixed number:

$\frac{21}{2} = 10\frac{1}{2}$

Therefore, the area of the rectangle is $10\frac{1}{2}$ square meters.