Understand Opposites on Number Line - 6th Grade Math

1. What is the opposite of $0$?

   $0$. Zero is its own opposite since it's neither positive nor negative.

2. What is the value of $-(-0)$?

   $0$. Zero remains zero regardless of how many opposites are taken.

3. What is the opposite of a number $a$ on the number line (in words)?

   The number the same distance from $0$ but on the other side. The opposite has equal distance from zero but opposite direction.

4. What is the opposite of $7$?

   $-7$. The opposite changes the sign from positive to negative.

5. Which statement is true: $-5$ is to the left of $0$, or $-5$ is to the right of $0$?

   $-5$ is to the left of $0$. Negative numbers are always positioned left of zero.

6. Which number is on the opposite side of $0$ from $-4$ but the same distance from $0$?

   $4$. Opposites are the same distance from zero on opposite sides.

7. What is the definition of the opposite of a number $a$ on a number line?

   The opposite of $a$ is $-a$, the same distance from $0$ on the other side. Opposites are equidistant from zero on opposite sides.

8. What is the value of $-\left(-\frac{7}{2}\right)$?

   $\frac{7}{2}$. Double negative of a fraction returns the positive fraction.

9. What is the distance between a number $a$ and its opposite $-a$ on the number line?

   $2|a|$. Each is $|a|$ units from zero, so total distance is twice that.

10. What is the opposite of $12$?

    $-12$. The opposite of a positive is the negative with same magnitude.

11. Which number is farther to the right on the number line: $-1$ or $-5$?

    $-1$. Among negatives, smaller absolute value means farther right.

12. What is the opposite of $\frac{5}{8}$?

    $-\frac{5}{8}$. The opposite flips the sign of the fraction.

13. What rule describes the opposite of the opposite of a number $a$?

    The opposite of the opposite of $a$ is $a$. Taking the opposite twice returns to the original number.

14. What is the opposite of $-12$?

    $12$. The opposite changes the sign from negative to positive.

15. What is the opposite of the opposite of a number $a$, written $-(-a)$?

    $a$. Taking the opposite twice returns the original number.

16. What is $-(-3)$?

    $3$. The opposite of the opposite returns the original number.

17. What is the value of $-(-15)$?

    $15$. The opposite of an opposite returns the original number.

18. Which statement is true: $6$ is to the left of $0$, or $6$ is to the right of $0$?

    $6$ is to the right of $0$. Positive numbers are always positioned right of zero.

19. What value makes this true: $x$ is the opposite of $13$?

    $x=-13$. The opposite of $13$ is the negative value $-13$.

20. What is $-(-25)$?

    $25$. Two negatives cancel out, returning the positive value.

21. What is the opposite of $-\frac{5}{8}$?

    $\frac{5}{8}$. Removing the negative sign gives the positive opposite.

22. Identify which is farther right on the number line: $-2$ or $3$?

    $3$. Positive numbers are always right of negative numbers.

23. Identify the number that is $3$ units from $0$ on the right side of the number line.

    $3$. Right of zero indicates a positive value.

24. Which number is the opposite of $-9$: $9$ or $-9$?

    $9$. The opposite of a negative number is positive.

25. What is the value of $-(8)$?

    $-8$. A negative sign makes a positive number negative.

26. What does a negative sign on a number indicate about its location relative to $0$ on a number line?

    It is located to the left of $0$ on the number line. Negative numbers are always positioned left of zero.

27. Which number is closer to $0$ on the number line: $-3$ or $5$?

    $-3$. Distance from zero is $|-3| = 3$ versus $|5| = 5$.

28. What is $-(-0.6)$?

    $0.6$. Double negatives cancel, yielding the positive value.

29. Which number is the opposite of $4$: $-4$ or $4$?

    $-4$. The opposite of a positive number is negative.

30. Identify which is farther left on the number line: $-8$ or $-1$?

    $-8$. Smaller negative numbers are farther left on the number line.

31. If a point is $8$ units to the left of $0$, what number names its location?

    $-8$. Points to the left of zero are negative numbers.

32. Which expression is equal to $4$: $-(-4)$ or $-(4)$?

    $-(-4)$. Double negative equals positive; single negative equals negative.

33. What is the distance between $-9$ and $9$ on the number line?

    $18$. Each number is $9$ units from zero: $9 + 9 = 18$.

34. What is the distance from $0$ to $-11$ on the number line?

    $11$ units. Distance is always positive, regardless of direction.

35. What does a positive sign on a number indicate about its location relative to $0$ on a number line?

    It is located to the right of $0$ on the number line. Positive numbers are always positioned right of zero.

36. Identify the number that is $3$ units from $0$ on the left side of the number line.

    $-3$. Left of zero indicates a negative value.

37. Which statement is true about $0$ and its opposite on the number line?

    $0$ is its own opposite. Zero is equidistant from itself on both sides.

38. What is the value of $-(-3)$?

    $3$. Two negatives cancel out, returning the original positive value.

39. What is the value of $-(-(-4))$?

    $-4$. Three negatives result in one negative: $-(-(-4)) = -4$.

40. What is the opposite of $-7$?

    $7$. The opposite changes the sign from negative to positive.

41. What is the opposite of the opposite of a number $a$, written as $-(-a)$?

    $-(-a)=a$. Taking the opposite twice returns the original number.

42. What is the opposite of a number $a$ on the number line?

    The number the same distance from $0$ on the other side, $-a$. The opposite has the same distance but on the other side of zero.

43. Identify the number that is its own opposite.

    $0$. Only zero equals its opposite since $-0 = 0$.

44. Which number is to the left on the number line: $-6$ or $2$?

    $-6$. Negative numbers are always left of positive numbers.

45. What is the opposite of $-(-0)$?

    $0$. Zero remains zero regardless of how many opposites are taken.

46. What does it mean on a number line when two numbers have opposite signs, such as $5$ and $-5$?

    They are the same distance from $0$ on opposite sides of $0$. Opposite signs place numbers equidistant from zero on different sides.

47. What does it mean on a number line if two numbers have opposite signs, like $5$ and $-5$?

    They are on opposite sides of $0$, the same distance from $0$. Opposite signs place numbers equidistant from zero on different sides.

48. If a point is $8$ units to the right of $0$, what number names its location?

    $8$. Points to the right of zero are positive numbers.

49. Identify the number that is the opposite of $\frac{3}{5}$

    $- \frac{3}{5}$. The opposite of a positive fraction is negative.

50. What value makes this true: $x$ is the opposite of $-6$?

    $x=6$. The opposite of $-6$ is the positive value $6$.

51. What is the opposite of $-0.6$?

    $0.6$. Opposites flip the sign while keeping the same distance from $0$.

52. Which number is on the opposite side of $0$ from $9$ but the same distance from $0$?

    $-9$. The opposite of positive $9$ is negative $9$.

53. Identify the number that is the opposite of $-0.4$.

    $0.4$. The opposite of a negative decimal is positive.

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