Question
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e. Shane designed a rectangular mural that is \( 2 \frac{3}{3} y a r d s ~ l o n g \) and \( 1 \frac{1}{3} \) yards high. What is the arev in square yards of the mural?

Ask by West Kelly. in the United States
Jan 24,2025

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Answer

The area of the mural is 4 square yards.

Solution

To find the area of Shane's rectangular mural, we'll use the formula for the area of a rectangle: \[ \text{Area} = \text{Length} \times \text{Height} \] ### Step 1: Convert Mixed Numbers to Improper Fractions 1. **Length:** \( 2 \frac{3}{3} \) yards \[ 2 \frac{3}{3} = 2 + \frac{3}{3} = 2 + 1 = 3 \text{ yards} \] 2. **Height:** \( 1 \frac{1}{3} \) yards \[ 1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \text{ yards} \] ### Step 2: Calculate the Area \[ \text{Area} = \text{Length} \times \text{Height} = 3 \times \frac{4}{3} \] \[ \text{Area} = \frac{12}{3} = 4 \text{ square yards} \] ### **Answer:** The area of the mural is **4 square yards**.

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The Deep Dive

To find the area of the mural, we need to multiply the length by the height. First, we convert the mixed numbers into improper fractions. The length of the mural is \(2 \frac{3}{3} = 3\) yards (since \( \frac{3}{3} = 1\) and adding to 2 gives us 3) and the height is \(1 \frac{1}{3} = \frac{4}{3}\) yards. Now, we calculate the area: \[ Area = Length \times Height = 3 \times \frac{4}{3} = 4 \text{ square yards}. \] So, the area of the mural is 4 square yards. To keep it interesting, imagine painting vibrant colors on that mural, transforming a plain wall into a captivating artwork! With a space of 4 square yards, you could depict a beautiful landscape or perhaps a lively jungle filled with animals. The possibilities are endless! And if you ever find yourself confused about converting mixed numbers to improper fractions, remember this simple tip: Multiply the whole number by the denominator, then add the numerator. It’s like a secret shortcut to making math a breeze!

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