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10. Smannah is making a quilt with squares that have side lengths of is foot each. Are the side lengths of the squares closer to \( \frac{1}{2} \) 16 foot or 1 foot long? Draw a diagram to support your answer.

Ask by Long Rowe. in the United States
Feb 21,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The side lengths of the squares are closer to 1 foot long.

Solution

To determine if the side lengths of the squares are closer to \( \frac{1}{2} \) foot or 1 foot, we can compare the two values. Given: - Side length of the squares = 1 foot To compare, we can calculate the difference between 1 foot and \( \frac{1}{2} \) foot. Difference = 1 foot - \( \frac{1}{2} \) foot Let's calculate the difference. Calculate the value by following steps: - step0: Calculate: \(1-\frac{1}{2}\) - step1: Reduce fractions to a common denominator: \(\frac{2}{2}-\frac{1}{2}\) - step2: Transform the expression: \(\frac{2-1}{2}\) - step3: Subtract the numbers: \(\frac{1}{2}\) The difference between 1 foot and \( \frac{1}{2} \) foot is \( \frac{1}{2} \) foot. Since the difference is \( \frac{1}{2} \) foot, the side lengths of the squares are closer to 1 foot than to \( \frac{1}{2} \) foot. Therefore, the side lengths of the squares are closer to 1 foot long.

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Beyond the Answer

To figure out if the side lengths of the squares (1 foot) are closer to \( \frac{1}{2} \) foot or 1 foot, we can simply compare their values. \( \frac{1}{2} \) foot is equivalent to 0.5 feet, and since 1 foot is obviously greater than 0.5 feet, the distance from 0.5 feet to 1 foot is \( 1 - 0.5 = 0.5 \) feet. Therefore, the squares are exactly 0 feet away from 1 foot but 0.5 feet away from \( \frac{1}{2} \) foot, making their side lengths closer to 1 foot. For a visual aid, imagine a line with 0 at the far left, 0.5 in the middle, and 1 at the far right. The point marked “1” is precisely where the squares lie, sitting snugly right on top of that point, proving they’re much closer to 1 foot than \( \frac{1}{2} \) foot!

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