Math Problem Statement
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]
Solution
Let's analyze each inequality in turn:
-
Choice A:
- On the number line, is to the left of and is to the right of .
- Since any negative number is less than any positive number, this inequality is correct.
-
Choice B:
- On the number line, is to the right of , and is to the left of .
- A positive number is always greater than a negative number, so this inequality is also correct.
-
Choice C:
- Both numbers are positive, but is greater than because .
- 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:
- What is the difference between a positive and a negative fraction?
- How do you compare two fractions on a number line?
- Why is any positive fraction always greater than a negative fraction?
- How does the sign of a fraction affect its value relative to zero?
- 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.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Number Line
Fraction Comparison
Formulas
None (conceptual comparison using number line)
Theorems
None (number comparison on a number line)
Suitable Grade Level
Grades 6-8