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

Q: Why can't I just multiply the whole numbers and fractions separately?

Because mixed numbers represent a single value, not separate parts! When you multiply $ 3\frac{1}{6} \times 2\frac{1}{3} $, you need to account for all combinations of multiplication, which only happens when you convert to improper fractions first.

Q: How do I convert a mixed number to an improper fraction?

Use the formula: Improper fraction = (whole × denominator + numerator) ÷ denominator. For $ 3\frac{1}{6} $: (3 × 6 + 1) ÷ 6 = $ \frac{19}{6} $

Q: Do I need to simplify the fraction before converting back?

Check if you can simplify first! For $ \frac{133}{18} $, since 133 and 18 share no common factors, it's already in simplest form. Then convert: 133 ÷ 18 = 7 remainder 7, so $ 7\frac{7}{18} $.

Q: How can I check if my area calculation is reasonable?

Estimate first! $ 3\frac{1}{6} $ is about 3, and $ 2\frac{1}{3} $ is about 2.3, so the area should be around 3 × 2.3 = 6.9. Our answer $ 7\frac{7}{18} $ ≈ 7.4 is close!

Q: What if I get confused with all the fraction operations?

Take it step by step:Step 1: Convert mixed → improper fractionsStep 2: Multiply straight acrossStep 3: Simplify if possibleStep 4: Convert back to mixed numberDon't rush - each step builds on the previous one!

Mixed Number Multiplication with Area Applications

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

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.
$3\frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{19}{6}$ $2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$

Step 2: Multiply the improper fractions.
$\frac{19}{6} \times \frac{7}{3} = \frac{19 \times 7}{6 \times 3} = \frac{133}{18}$

Step 3: Simplify the resulting fraction, if possible.

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

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

Final Answer

$7\frac{7}{18}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Transform mixed numbers to improper fractions before multiplying
Technique: Multiply numerators together and denominators together: $\frac{19}{6} \times \frac{7}{3} = \frac{133}{18}$
Check: Convert final answer back to mixed number and verify reasonableness ✓

Common Mistakes

Avoid these frequent errors

Multiplying whole parts and fraction parts separately
Don't multiply 3 × 2 = 6 and $\frac{1}{6} \times \frac{1}{3} = \frac{1}{18}$ then add = wrong answer of $6\frac{1}{18}$ ! This ignores the cross-multiplication between whole and fractional parts. Always convert to improper fractions first, then multiply.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{3}\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

Why can't I just multiply the whole numbers and fractions separately?

Because mixed numbers represent a single value, not separate parts! When you multiply $3\frac{1}{6} \times 2\frac{1}{3}$ , you need to account for all combinations of multiplication, which only happens when you convert to improper fractions first.

How do I convert a mixed number to an improper fraction?

Use the formula: Improper fraction = (whole × denominator + numerator) ÷ denominator. For $3\frac{1}{6}$ : (3 × 6 + 1) ÷ 6 = $\frac{19}{6}$

Do I need to simplify the fraction before converting back?

Check if you can simplify first! For $\frac{133}{18}$ , since 133 and 18 share no common factors, it's already in simplest form. Then convert: 133 ÷ 18 = 7 remainder 7, so $7\frac{7}{18}$ .

How can I check if my area calculation is reasonable?

Estimate first! $3\frac{1}{6}$ is about 3, and $2\frac{1}{3}$ is about 2.3, so the area should be around 3 × 2.3 = 6.9. Our answer $7\frac{7}{18}$ ≈ 7.4 is close!

What if I get confused with all the fraction operations?

Take it step by step:

Step 1: Convert mixed → improper fractions
Step 2: Multiply straight across
Step 3: Simplify if possible
Step 4: Convert back to mixed number

Don't rush - each step builds on the previous one!

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