Calculate Rectangle Area: 4⅓ Meters × 2¾ Meters

Question

What is the area of the rectangle whose length 413 4\frac{1}{3} meters and the width 234 2\frac{3}{4} ?

Video Solution

Solution Steps

00:00 Find the area of the rectangle
00:03 Use the formula to calculate the rectangle's area
00:06 Side times side, substitute the side lengths according to the given data
00:12 Convert mixed numbers to fractions
00:22 Always solve multiplication and division before addition and subtraction
00:37 Make sure to multiply numerator by numerator and denominator by denominator
00:43 Calculate the products
00:51 Break down into whole number and remainder
01:03 Convert whole fraction to whole number
01:11 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll calculate the area of a rectangle given in mixed numbers using these steps:

  • Step 1: Convert mixed numbers to improper fractions.
  • Step 2: Multiply the improper fractions to find the area.
  • Step 3: Simplify the resulting fraction and convert it back to a mixed number if possible.

Let's proceed with each step:

Step 1: Convert mixed numbers to improper fractions.
Given length 413 4\frac{1}{3} meters and width 234 2\frac{3}{4} meters, we convert each:

413=133,234=114 4\frac{1}{3} = \frac{13}{3}, \quad 2\frac{3}{4} = \frac{11}{4}

Step 2: Multiply the improper fractions to calculate the area.
Area=133×114=13×113×4=14312 \text{Area} = \frac{13}{3} \times \frac{11}{4} = \frac{13 \times 11}{3 \times 4} = \frac{143}{12}

Step 3: Simplify 14312\frac{143}{12} and convert to a mixed number.
Divide 143 by 12:

143÷12=11remainder11 143 \div 12 = 11 \quad \text{remainder} \, 11

So, 14312=111112\frac{143}{12} = 11\frac{11}{12}

Therefore, the area of the rectangle is 131112 13\frac{11}{12} square meters.

Answer

131112 13\frac{11}{12}