Which of the following inequalities are correct?
Some of the numbers involved are shown on the number line below.
Choose all answers that apply:
Choose all answers that apply:
(Choice A, Checked)   
 
 
\[-\dfrac{5}6\,\,<\,\,\,\,\,\ \dfrac{1}6\]
A
 
 
\[-\dfrac{5}6\,\,<\,\,\,\,\,\ \dfrac{1}6\]
(Choice B, Checked)   
 
 
\[\,\,\,\,\,\dfrac{5}6\,\,>\, -\dfrac{1}6\]
B
 
 
\[\,\,\,\,\,\dfrac{5}6\,\,>\, -\dfrac{1}6\]
(Choice C, Checked)   
 
 
\[\,\,\,\,\,\dfrac{5}6\,\,>\,\,\,\,\,\ \dfrac{1}6\]
C
 
 
\[\,\,\,\,\,\dfrac{5}6\,\,>\,\,\,\,\,\ \dfrac{1}6\]
A number line from negative 1 to 1 with evenly spaced tick marks in increments of 1 sixth.  The first tick mark to the left of 0 is labeled negative 1 sixth. The first tick mark to the left of 1 is labeled 5 sixths.
\[0\]
 
\[\frac56\]


Let's analyze each inequality in turn:

1. **Choice A:**
   \[
   -\dfrac{5}{6} < \dfrac{1}{6}
   \]
   - On the number line, \(-\dfrac{5}{6}\) is to the left of \(0\) and \(\dfrac{1}{6}\) is to the right of \(0\).
   - Since any negative number is less than any positive number, this inequality is correct.

2. **Choice B:**
   \[
   \dfrac{5}{6} > -\dfrac{1}{6}
   \]
   - On the number line, \(\dfrac{5}{6}\) is to the right of \(0\), and \(-\dfrac{1}{6}\) is to the left of \(0\).
   - A positive number is always greater than a negative number, so this inequality is also correct.

3. **Choice C:**
   \[
   \dfrac{5}{6} > \dfrac{1}{6}
   \]
   - Both numbers are positive, but \(\dfrac{5}{6}\) is greater than \(\dfrac{1}{6}\) because \(5 > 1\).
   - Therefore, this inequality is correct.

### Conclusion:
- All three inequalities (Choices A, B, and C) are correct.

Let me know if you'd like any further clarification on this.

### Relative Questions:
1. What is the difference between a positive and a negative fraction?
2. How do you compare two fractions on a number line?
3. Why is any positive fraction always greater than a negative fraction?
4. How does the sign of a fraction affect its value relative to zero?
5. What is the importance of number line visualization in comparing inequalities?

### Tip:
When comparing fractions, converting them to decimals or visualizing them on a number line can help you easily determine which is greater.

Which of the following inequalities are correct? Some of the numbers involved are shown on the number line below. Choose all answers that apply: (Choice A) -5/6 < 1/6, (Choice B) 5/6 > -1/6, (Choice C) 5/6 > 1/6.

Understand how to compare fractions and inequalities using a number line. This problem involves determining the correctness of inequalities like -5/6 < 1/6 and 5/6 > -1/6. Suitable for students in Grades 6-8, this exercise covers fraction comparison and visualization techniques.

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