https://file.aiquickdraw.com/mathbot/file/1728400562793sw8h8lwc.jpg

The problem asks to calculate the area of a rectangle using the given dimensions in mixed numbers. 

The length is \( 5 \frac{1}{6} \) cm and the width is \( 2 \frac{2}{7} \) cm. The area of a rectangle is calculated as:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

### Step 1: Convert the mixed numbers to improper fractions
- \( 5 \frac{1}{6} = \frac{31}{6} \)
- \( 2 \frac{2}{7} = \frac{16}{7} \)

### Step 2: Multiply the improper fractions
\[
\frac{31}{6} \times \frac{16}{7} = \frac{31 \times 16}{6 \times 7} = \frac{496}{42}
\]

### Step 3: Simplify the fraction
\[
\frac{496}{42} = \frac{248}{21} \quad \text{(after dividing numerator and denominator by 2)}
\]

### Step 4: Convert the improper fraction to a mixed number
\[
\frac{248}{21} = 11 \frac{17}{21}
\]

Thus, the area of the rectangle is \( 11 \frac{17}{21} \) square centimeters.

Would you like more details on any part of this solution?

Here are some related questions to deepen understanding:
1. How do you convert a mixed number to an improper fraction?
2. Why is simplifying fractions important when solving problems like this?
3. Can you show how to multiply fractions step-by-step in detail?
4. How can we convert an improper fraction back into a mixed number?
5. What is the practical significance of the area in this problem?

**Tip:** When converting mixed numbers to improper fractions, remember to multiply the whole number by the denominator and then add the numerator!

Work out the area of the rectangle using a calculator and giving your answer as a mixed number. The dimensions of the rectangle are 5 1/6 cm and 2 2/7 cm.

Learn how to calculate the area of a rectangle with mixed number dimensions (5 1/6 cm by 2 2/7 cm) by converting mixed numbers to improper fractions, multiplying them, and simplifying the result. This step-by-step guide is perfect for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation