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In 1 and 2 , choose from the fractions \( \frac{1}{3}, \frac{5}{6}, \frac{3}{4} \), and \( \frac{3}{8} \). 1. Which of the fractions are closer to 1 than to 0 ? 2. Which of the fractions are closer to 0 than to 1 ? 3. Write two fractions with a denominator of 8 that are than to 1 .

Ask by George Ellis. in the United States
Mar 08,2025

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Answer

1. Fractions closer to 1 than to 0: \( \frac{5}{6}, \frac{3}{4} \) 2. Fractions closer to 0 than to 1: \( \frac{1}{3}, \frac{3}{8} \) 3. Two fractions with a denominator of 8 closer to 1 than to 0: \( \frac{5}{8}, \frac{6}{8} \)

Solution

Let's analyze the fractions given: \( \frac{1}{3}, \frac{5}{6}, \frac{3}{4}, \frac{3}{8} \). ### Step 1: Determine which fractions are closer to 1 than to 0. To find out if a fraction is closer to 1 than to 0, we can check if it is greater than \( \frac{1}{2} \). - \( \frac{1}{3} \approx 0.33 \) (less than \( \frac{1}{2} \)) - \( \frac{5}{6} \approx 0.83 \) (greater than \( \frac{1}{2} \)) - \( \frac{3}{4} = 0.75 \) (greater than \( \frac{1}{2} \)) - \( \frac{3}{8} \approx 0.375 \) (less than \( \frac{1}{2} \)) **Fractions closer to 1 than to 0:** \( \frac{5}{6}, \frac{3}{4} \) ### Step 2: Determine which fractions are closer to 0 than to 1. Using the same criterion, we check which fractions are less than \( \frac{1}{2} \): - \( \frac{1}{3} \approx 0.33 \) (less than \( \frac{1}{2} \)) - \( \frac{5}{6} \approx 0.83 \) (greater than \( \frac{1}{2} \)) - \( \frac{3}{4} = 0.75 \) (greater than \( \frac{1}{2} \)) - \( \frac{3}{8} \approx 0.375 \) (less than \( \frac{1}{2} \)) **Fractions closer to 0 than to 1:** \( \frac{1}{3}, \frac{3}{8} \) ### Step 3: Write two fractions with a denominator of 8 that are closer to 1 than to 0. To find fractions with a denominator of 8 that are closer to 1 than to 0, we need to find fractions greater than \( \frac{1}{2} \) (which is \( \frac{4}{8} \)). Possible fractions with a denominator of 8 that are greater than \( \frac{4}{8} \) include: - \( \frac{5}{8} \) - \( \frac{6}{8} \) - \( \frac{7}{8} \) **Two fractions with a denominator of 8 that are closer to 1 than to 0:** \( \frac{5}{8}, \frac{6}{8} \) (or \( \frac{7}{8} \) as well). ### Summary: 1. Fractions closer to 1 than to 0: \( \frac{5}{6}, \frac{3}{4} \) 2. Fractions closer to 0 than to 1: \( \frac{1}{3}, \frac{3}{8} \) 3. Two fractions with a denominator of 8 that are closer to 1 than to 0: \( \frac{5}{8}, \frac{6}{8} \)

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1. The fractions that are closer to 1 than to 0 are \( \frac{5}{6} \) and \( \frac{3}{4} \). Both of these values are greater than \( \frac{1}{2} \) but less than 1, making them closer to 1 on the number line. 2. The fractions that are closer to 0 than to 1 are \( \frac{1}{3} \) and \( \frac{3}{8} \). These values are less than \( \frac{1}{2} \), placing them nearer to 0 compared to 1 when you look at their positions on the number line. 3. Two fractions with a denominator of 8 that are closer to 0 than to 1 are \( \frac{1}{8} \) and \( \frac{3}{8} \). Both of these fractions represent values less than \( \frac{1}{2} \), making them closer to 0.

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