Final answer:
The true statements are that 0 is greater than -2/3, -1 is less than -1/3, and -1/3 is greater than -2/3. These are true because of the order of numbers on the number line and the fact that zero is greater than any negative number.
To determine which statements are true, let's check each one:
O is greater than -2/3: This statement is true because 0 is greater than any negative number.
2/3 is equal to -2/3: This statement is false because 2/3 is not equal to -2/3.
-2/3 - 1 < -1/3: This statement is true because -2/3 - 1 is indeed less than -1/3.
-2/3 > 1/3: This statement is false because -2/3 is less than 1/3.
1/3 - 1/3 > -2/3: This statement is true because 1/3 - 1/3 is equal to 0, which is greater than -2/3.
In summary, the true statements are: O is greater than -2/3 and -2/3 - 1 < -1/3, and 1/3 - 1/3 > -2/3.
Step-by-step explanation:
Let's evaluate each statement one by one to determine if they are true:
- 0 is greater than -2/3: True. Zero (0) is greater than any negative number, including -2/3.
- 2/3 is equal to -2/3: False. 2/3 is positive while -2/3 is negative, therefore, they cannot be equal.
- -1 < -1/3: True. -1 is less than -1/3 because as we move to the right on the number line, the value increases even with negative numbers.
- -2/3 > 1/3: False. -2/3 is negative and 1/3 is positive, so -2/3 is less than 1/3.
- -1/3 > -2/3: True. As stated earlier, moving to the right on the number line increases value, therefore -1/3 is greater than -2/3.
In conclusion, the true statements are: 0 is greater than -2/3, -1 < -1/3, and -1/3 > -2/3.