Question
identify the numeric order of these fractions from the smallest to largest 3/6, 1/6, 5/6 and 2/6 A 1/6, 2/6, 3/6 and 5/6 B 30/36 18/36, 12/36 and 6/36 C 3/6, 2/6, 1/6 and 5/6 D 15/30 6, 5/6, 6/36, and 2/6
Answers
GPT-4o mini
To identify the numeric order of the fractions from smallest to largest, let's first convert all the fractions to have a common denominator or convert them to decimal form.
1. **Convert to Decimal:**
- \( \frac{1}{6} \approx 0.1667 \)
- \( \frac{2}{6} = \frac{1}{3} \approx 0.3333 \)
- \( \frac{3}{6} = \frac{1}{2} = 0.5 \)
- \( \frac{5}{6} \approx 0.8333 \)
Now we can order them:
- \( \frac{1}{6} < \frac{2}{6} < \frac{3}{6} < \frac{5}{6} \)
So from smallest to largest, the order is:
1. \( \frac{1}{6} \)
2. \( \frac{2}{6} \)
3. \( \frac{3}{6} \)
4. \( \frac{5}{6} \)
### Answer:
**A) \( \frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{5}{6} \)**
Let's briefly examine the other options for their similarity to the fractions given:
B) \( \frac{30}{36}, \frac{18}{36}, \frac{12}{36}, \frac{6}{36} \) can be simplified as follows:
- \( \frac{30}{36} = \frac{5}{6} \)
- \( \frac{18}{36} = \frac{1}{2} \)
- \( \frac{12}{36} = \frac{1}{3} \)
- \( \frac{6}{36} = \frac{1}{6} \)
The order is \( \frac{6}{36} < \frac{12}{36} < \frac{18}{36} < \frac{30}{36} \), which translates to:
- \( \frac{1}{6} < \frac{1}{3} < \frac{1}{2} < \frac{5}{6} \)
C) The fractions are repeated as in option A in reverse order, which is incorrect.
D) \( \frac{15}{30} \) simplifies to \( \frac{1}{2} \). \( \frac{6}{36} = \frac{1}{6} \) and \( \frac{5}{6} \) doesn't fit the order as \( \frac{2}{6} \) would be the missing element in the context of ordering.
Thus, the correct sequence is confirmed to be:
**A) \( \frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{5}{6} \)**.
1. **Convert to Decimal:**
- \( \frac{1}{6} \approx 0.1667 \)
- \( \frac{2}{6} = \frac{1}{3} \approx 0.3333 \)
- \( \frac{3}{6} = \frac{1}{2} = 0.5 \)
- \( \frac{5}{6} \approx 0.8333 \)
Now we can order them:
- \( \frac{1}{6} < \frac{2}{6} < \frac{3}{6} < \frac{5}{6} \)
So from smallest to largest, the order is:
1. \( \frac{1}{6} \)
2. \( \frac{2}{6} \)
3. \( \frac{3}{6} \)
4. \( \frac{5}{6} \)
### Answer:
**A) \( \frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{5}{6} \)**
Let's briefly examine the other options for their similarity to the fractions given:
B) \( \frac{30}{36}, \frac{18}{36}, \frac{12}{36}, \frac{6}{36} \) can be simplified as follows:
- \( \frac{30}{36} = \frac{5}{6} \)
- \( \frac{18}{36} = \frac{1}{2} \)
- \( \frac{12}{36} = \frac{1}{3} \)
- \( \frac{6}{36} = \frac{1}{6} \)
The order is \( \frac{6}{36} < \frac{12}{36} < \frac{18}{36} < \frac{30}{36} \), which translates to:
- \( \frac{1}{6} < \frac{1}{3} < \frac{1}{2} < \frac{5}{6} \)
C) The fractions are repeated as in option A in reverse order, which is incorrect.
D) \( \frac{15}{30} \) simplifies to \( \frac{1}{2} \). \( \frac{6}{36} = \frac{1}{6} \) and \( \frac{5}{6} \) doesn't fit the order as \( \frac{2}{6} \) would be the missing element in the context of ordering.
Thus, the correct sequence is confirmed to be:
**A) \( \frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{5}{6} \)**.