Calculate Area: 5½ Meters × ⅔ Meter Rectangle Problem

Q: Why do I need to convert the mixed number to an improper fraction?

Converting $ 5\frac{1}{2} $ to $ \frac{11}{2} $ makes multiplication much easier! You can't directly multiply a mixed number by a fraction without converting first.

Q: Can I leave my answer as an improper fraction?

You can, but mixed numbers are usually preferred for area problems. $ 3\frac{2}{3} $ square meters is easier to visualize than $ \frac{11}{3} $ square meters.

Q: What if I forget to include square meters in my answer?

Always include units! Since you're multiplying meters × meters, your answer must be in square meters. Area always has squared units.

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

Estimate first: $ 5\frac{1}{2} $ is about 6, and $ \frac{2}{3} $ is about 0.7, so 6 × 0.7 ≈ 4.2. Our answer $ 3\frac{2}{3} $ ≈ 3.67 is close!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the area of the pool

00:03 We'll use the formula for calculating the area of a rectangle

00:07 Side times side, we'll input the lengths of the sides according to the given data

00:13 Convert mixed fraction to fraction

00:25 Make sure to multiply numerator by numerator and denominator by denominator

00:33 Calculate the multiplications

00:39 Reduce the fraction as much as possible

00:43 Make sure to divide both numerator and denominator

00:50 This is the solution to the fraction problem

00:55 Break down the numerator into whole number and remainder

01:02 Convert whole fraction to whole number

01:10 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

What is the area of a pool that has a length of $5\frac{1}{2}$ meters and a width of $\frac{2}{3}$ of a meter?

2

Step-by-step solution

To solve this problem, we need to find the area of a pool with a given length and width.

Step 1: Convert the mixed number to an improper fraction.
Step 2: Multiply the two fractions to find the area.
Step 3: Simplify the result if necessary.

First, let's convert the length from a mixed number to an improper fraction. The length is $5\frac{1}{2}$ meters, which can be written as an improper fraction:

5\frac{1}{2} = \frac{11}{2}

The width is already given as a fraction: $\frac{2}{3}$ meters.

Step 2: To find the area of the pool, we multiply the length by the width:

\text{Area} = \left(\frac{11}{2}\right) \times \left(\frac{2}{3}\right)

Now, multiply the numerators together and the denominators together:

\text{Area} = \frac{11 \times 2}{2 \times 3} = \frac{22}{6}

Step 3: Let's simplify $\frac{22}{6}$ . The greatest common divisor of 22 and 6 is 2, so dividing the numerator and the denominator by 2 gives:

\frac{22 \div 2}{6 \div 2} = \frac{11}{3}

This can be further expressed as a mixed number:

\frac{11}{3} = 3\frac{2}{3}

Therefore, the area of the pool is $3\frac{2}{3}$ square meters.

3

Final Answer

$3\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Convert: Change mixed numbers to improper fractions before multiplying
Multiply: $\frac{11}{2} \times \frac{2}{3} = \frac{22}{6}$ by multiplying across
Simplify: Reduce $\frac{22}{6} = \frac{11}{3} = 3\frac{2}{3}$ and verify units ✓

Common Mistakes

Avoid these frequent errors

Adding fractions instead of multiplying for area
Don't add $5\frac{1}{2} + \frac{2}{3} = 6\frac{1}{6}$ ! This gives perimeter, not area. Area problems always require multiplication. Always multiply length × width for rectangular areas.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{4}\times\frac{3}{2}=$

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number to an improper fraction?

+

Converting $5\frac{1}{2}$ to $\frac{11}{2}$ makes multiplication much easier! You can't directly multiply a mixed number by a fraction without converting first.

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

+

Multiply the whole number by the denominator, then add the numerator: $5\frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{11}{2}$

Can I leave my answer as an improper fraction?

+

You can, but mixed numbers are usually preferred for area problems. $3\frac{2}{3}$ square meters is easier to visualize than $\frac{11}{3}$ square meters.

What if I forget to include square meters in my answer?

+

Always include units! Since you're multiplying meters × meters, your answer must be in square meters. Area always has squared units.

How can I check if my area calculation is reasonable?

+

Estimate first: $5\frac{1}{2}$ is about 6, and $\frac{2}{3}$ is about 0.7, so 6 × 0.7 ≈ 4.2. Our answer $3\frac{2}{3}$ ≈ 3.67 is close!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Calculate Area: 5½ Meters × ⅔ Meter Rectangle Problem

Fraction Multiplication with Mixed Numbers

❤️ Continue Your Math Journey!