Calculate Rectangle Area: 3 1/6 m × 2 1/3 m Mixed Number Multiplication

Question

What is the area of the rectangle whose length 316 3\frac{1}{6} meters and the width 213 2\frac{1}{3} ?

Video Solution

Solution Steps

00:00 Find the area of the rectangle
00:04 Use the formula to calculate the rectangle's area
00:08 Side times side, substitute the side lengths according to the data
00:14 Convert mixed numbers to fractions
00:31 Make sure to multiply numerator by numerator and denominator by denominator
00:38 Calculate the products
00:50 Break down into whole number and remainder
01:01 Convert whole fraction to whole number
01:10 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert the mixed numbers to improper fractions.
  • Step 2: Multiply the improper fractions.
  • Step 3: Simplify the resulting fraction.
  • Step 4: Convert back to a mixed number if required.

Now, let's work through each step:

Step 1: Convert the mixed numbers to improper fractions.
316=3×6+16=196 3\frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{19}{6} 213=2×3+13=73 2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}

Step 2: Multiply the improper fractions.
196×73=19×76×3=13318 \frac{19}{6} \times \frac{7}{3} = \frac{19 \times 7}{6 \times 3} = \frac{133}{18}

Step 3: Simplify the resulting fraction, if possible.

Step 4: Convert back to a mixed number, since 13318\frac{133}{18} is an improper fraction:
Divide 133 by 18 to get the mixed number:
133÷18=7133 \div 18 = 7 remainder 77.
Thus, 13318=7718\frac{133}{18} = 7\frac{7}{18}.

Therefore, the area of the rectangle is 77187\frac{7}{18} square meters.

Answer

7718 7\frac{7}{18}