A number line going from negative 1 to positive 1 in increments of 1. There are 3 equal spaces between each number.

Question

Which statements are true? Check all that apply.
0 is greater than Negative two-thirds.
Two-thirds is equal to Negative two-thirds.
Negative 1 less-than negative one-third
Negative two-thirds greater-than one-third
Negative one-third greater-than negative two-thirds

Answer 1

Let's analyze each statement one by one to determine if they are true or false:

1. 0 is greater than Negative two-thirds.
   True: Since 0 is greater than any negative number, this statement is true.

2. Two-thirds is equal to Negative two-thirds.
   False: \(\frac{2}{3}\) is a positive number, while \(-\frac{2}{3}\) is a negative number. They are not equal.

3. Negative 1 less-than negative one-third.
   True: \(-1\) is less than \(-\frac{1}{3}\), as \(-1\) is further to the left on the number line.

4. Negative two-thirds greater-than one-third.
   False: \(-\frac{2}{3}\) is a negative number, and \(\frac{1}{3}\) is a positive number, so \(-\frac{2}{3}\) is less than \(\frac{1}{3}\).

5. Negative one-third greater-than negative two-thirds.
   True: \(-\frac{1}{3}\) is closer to 0 than \(-\frac{2}{3}\), so \(-\frac{1}{3}\) is greater than \(-\frac{2}{3}\).

Based on the analysis above, the true statements are:

• 0 is greater than Negative two-thirds.
• Negative 1 less-than negative one-third.
• Negative one-third greater-than negative two-thirds.