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:

  1. Choice A: 56<16-\dfrac{5}{6} < \dfrac{1}{6}

    • On the number line, 56-\dfrac{5}{6} is to the left of 00 and 16\dfrac{1}{6} is to the right of 00.
    • Since any negative number is less than any positive number, this inequality is correct.
  2. Choice B: 56>16\dfrac{5}{6} > -\dfrac{1}{6}

    • On the number line, 56\dfrac{5}{6} is to the right of 00, and 16-\dfrac{1}{6} is to the left of 00.
    • A positive number is always greater than a negative number, so this inequality is also correct.
  3. Choice C: 56>16\dfrac{5}{6} > \dfrac{1}{6}

    • Both numbers are positive, but 56\dfrac{5}{6} is greater than 16\dfrac{1}{6} because 5>15 > 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.

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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