Examine where the two fractions are plotted on the number line.

Question

A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. A point is 1 mark to the left of 0, and another point is 1 mark to the right of 0.

Which statements are true? Select all that apply.
One-fourth greater-than negative one-fourth
One-fourth less-than negative one-fourth
Negative one-fourth greater-than one-fourth
Negative one-fourth less-than one-fourth
Negative one-fourth = one-fourth

Answer 1

Let's analyze the two fractions: \( \frac{1}{4} \) (one-fourth) and \( -\frac{1}{4} \) (negative one-fourth).

On the number line, \( \frac{1}{4} \) is to the right of 0, while \( -\frac{1}{4} \) is to the left of 0.

Now, let's evaluate each statement:

1. One-fourth greater than negative one-fourth: \(\frac{1}{4} > -\frac{1}{4}\) is true.

2. One-fourth less than negative one-fourth: \(\frac{1}{4} < -\frac{1}{4}\) is false.

3. Negative one-fourth greater than one-fourth: \(-\frac{1}{4} > \frac{1}{4}\) is false.

4. Negative one-fourth less than one-fourth: \(-\frac{1}{4} < \frac{1}{4}\) is true.

5. Negative one-fourth = one-fourth: \(-\frac{1}{4} = \frac{1}{4}\) is false.

Based on this analysis, the true statements are:

• One-fourth greater than negative one-fourth
• Negative one-fourth less than one-fourth