A Rectangle Is $\frac{1}{3}$ Yards Long And $\frac{2}{3}$ Yards Wide.What Is The Area Of The Rectangle?Enter Your Answer As A Fraction In Simplest Form By Filling In The Boxes: □ Y D 2 \square \, Yd^2 □ Y D 2

Mar 10, 2025 by ADMIN 213 views

**Calculating the Area of a Rectangle: A Step-by-Step Guide**

Understanding the Problem

When it comes to calculating the area of a rectangle, we need to consider the length and width of the rectangle. In this problem, we are given that the rectangle is $\frac{1}{3}$ yards long and $\frac{2}{3}$ yards wide. To find the area of the rectangle, we need to multiply the length and width together.

The Formula for Area

The formula for the area of a rectangle is:

Area = Length x Width

In this case, the length is $\frac{1}{3}$ yards and the width is $\frac{2}{3}$ yards. So, we can plug these values into the formula:

Area = $\frac{1}{3}$ x $\frac{2}{3}$

Multiplying Fractions

To multiply fractions, we need to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) together. So, we can multiply $\frac{1}{3}$ and $\frac{2}{3}$ as follows:

$\frac{1}{3}$ x $\frac{2}{3}$ = $\frac{1 x 2}{3 x 3}$

Simplifying the Fraction

Now that we have multiplied the fractions, we can simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 2 and 3 is 1, so we can simplify the fraction as follows:

$\frac{1 x 2}{3 x 3}$ = $\frac{2}{9}$

Conclusion

Therefore, the area of the rectangle is $\frac{2}{9}$ square yards.

Real-World Applications

Calculating the area of a rectangle is an important skill that has many real-world applications. For example, if you are a contractor or builder, you may need to calculate the area of a room or a piece of land in order to determine how much material you will need to buy. Similarly, if you are a gardener or landscaper, you may need to calculate the area of a garden or a lawn in order to determine how much fertilizer or other supplies you will need.

Tips and Tricks

Here are a few tips and tricks to help you calculate the area of a rectangle:

Make sure to multiply the length and width together correctly.
Simplify the fraction by dividing both the numerator and the denominator by their GCD.
Use a calculator or a spreadsheet to help you with the calculation if you are unsure.

Common Mistakes

Here are a few common mistakes to avoid when calculating the area of a rectangle:

Not multiplying the length and width together correctly.
Not simplifying the fraction correctly.
Not using a calculator or a spreadsheet to help with the calculation.

Conclusion

In conclusion, calculating the area of a rectangle is a simple but important skill that has many real-world applications. By following the steps outlined in this article, you should be able to calculate the area of a rectangle with ease. Remember to multiply the length and width together correctly, simplify the fraction by dividing both the numerator and the denominator by their GCD, and use a calculator or a spreadsheet to help with the calculation if you are unsure.

Final Answer

The final answer is: $\boxed{\frac{2}{9}}$