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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