Distinguish Absolute Value From Order - 6th Grade Math

1. Which is true: $-4 < 3$ or $|-4| < |3|$?

   $-4 < 3$. Order comparison: negative is less than positive.

2. Choose the correct statement: Is $-7$ to the left or right of $-2$ on a number line?

   Left. Negative numbers increase as you move right.

3. Which statement must be true if $|a| > |b|$: $a > b$ or $a$ is farther from $0$ than $b$?

   $a$ is farther from $0$ than $b$. Greater absolute value means greater distance from zero.

4. Choose the correct sign: $|-2| \; \square \; |-5|$ where $\square$ is $<$, $>$, or $=$.

   $|-2| < |-5|$. $|-2| = 2$ and $|-5| = 5$, so 2 < 5.

5. Find and correct the statement if needed: "$-10 > -2$ because $|-10| > |-2|$."

   Correct: $-10 < -2$ even though $|-10| > |-2|$. Order and distance are different: -10 is left of -2.

6. Which number is greater: $-3$ or $2$?

   $2$. Positive numbers are always greater than negatives.

7. Which pair has the same absolute value: $-8$ and $8$, or $-8$ and $-7$?

   $-8$ and $8$. $|-8| = 8$ and $|8| = 8$, both are 8 units from zero.

8. Which inequality correctly compares distances from $0$: $|-3| \; \square \; |1|$?

   $|-3| > |1|$. $|-3| = 3$ and $|1| = 1$, so 3 > 1.

9. Choose the correct sign: $-2 \; \square \; -5$ where $\square$ is $<$, $>$, or $=$.

   $-2 > -5$. -2 is to the right of -5 on the number line.

10. What is the correct conclusion if $|x| = 4$? State all possible values of $x$.

    $x = 4$ or $x = -4$. Absolute value 4 means 4 units from zero in either direction.

11. Identify which number is larger: $-5$ or $3$.

    $3$. Positive 3 is to the right of negative 5 on the number line.

12. Choose the true statement: $-5 < -1$ or $|-5| < |-1|$?

    $|-5| < |-1|$ is false; $|-5| > |-1|$ is true. $|-5| = 5$ and $|-1| = 1$, so $5 > 1$.

13. Which number is closer to $0$: $-1$ or $2$?

    $-1$. $|-1| = 1$ and $|2| = 2$, so -1 is 1 unit from zero.

14. Which statement matches: "$x$ is to the left of $y$ on the number line"?

    $x < y$. Left position means smaller value.

15. Which statement matches: "$x$ is closer to $0$ than $y$"?

    $|x| < |y|$. Smaller absolute value means closer to zero.

16. What does the inequality $a < b$ compare: order on the number line or distance from $0$?

    Order on the number line (left-right position). Without absolute value bars, we compare positions on the number line.

17. Which statement is about distance from $0$: $-7 < -3$ or $|-7| > |-3|$?

    $|-7| > |-3|$. Absolute value bars show distance: 7 units > 3 units from zero.

18. Identify which is larger: $| -5 |$ or $| 3 |$.

    $|-5|$. $|-5| = 5$ and $|3| = 3$, so 5 > 3.

19. What does the inequality $|a| < |b|$ compare: order or distance from $0$?

    Distance from $0$ (absolute value), not order. Absolute value measures distance, not position.

20. What does the statement $a > b$ describe: distance from $0$ or position (order) on the number line?

    Position (order): $a$ is to the right of $b$. Order compares positions on the number line.

21. Which statement is about order on the number line: $-7 < -3$ or $|-7| > |-3|$?

    $-7 < -3$. No absolute value bars means comparing positions: -7 is left of -3.

22. Find the correct order statement using $<$ or $>$: Compare $-10$ and $-12$.

    $-10 > -12$. For negatives, less negative means greater.

23. Which number is greater: $-7$ or $-2$?

    $-2$. On the number line, $-2$ is to the right of $-7$.

24. Which number is farther from $0$: $-9$ or $6$?

    $-9$. $|-9| = 9 > 6 = |6|$, so $-9$ is farther.

25. Identify the true statement: $-6 > -2$ or $|-6| > |-2|$?

    $|-6| > |-2|$. $|-6| = 6 > 2 = |-2|$, but $-6 < -2$ in order.

26. Identify the correct statement: If $a<0$, what is $|a|$ equal to?

    $|a|=-a$. For negative numbers, absolute value equals the opposite.

27. Which statement is about absolute value: $-3 < 2$ or $|-3| < |2|$?

    $|-3| < |2|$. Compares distances from zero.

28. Which is true: $-4 < 3$ or $|-4| > |3|$?

    $|-4| > |3|$. Both statements are true; $4 > 3$ in absolute value.

29. Identify the true statement: If $|a| > |b|$, then $a > b$ is always true. True or false?

    False. Example: $|-5| > |3|$ but $-5 < 3$.

30. Which is greater: $-4$ or $3$?

    $3$. Positive numbers are always greater than negative numbers.

31. What does the statement $|a| > |b|$ compare: location on the number line or distance from $0$?

    Distance from $0$ (magnitude), not left-right order. Absolute value measures how far from zero, not position.

32. Find the correct absolute value comparison: Compare $|-10|$ and $|-12|$ using $<$ or $>$.

    $|-10| < |-12|$. $|-10| = 10 < 12 = |-12|$.

33. Which absolute value is greater: $|-7|$ or $|-2|$?

    $|-7|$. $|-7| = 7$ and $|-2| = 2$, so $7 > 2$.

34. Identify the correct conclusion: If $|a| = |b|$, what can be true about $a$ and $b$?

    $a=b$ or $a=-b$. Equal distances can be in opposite directions.

35. Which comparison is true: $-9 < -4$ or $|-9| < |-4|$?

    $-9 < -4$. On the number line, -9 is to the left of -4.

36. Which inequality compares distances from $0$: $|a| < |b|$ or $a < b$?

    $|a| < |b|$. Absolute value bars compare distances from zero.

37. Which number is greater (to the right on the number line): $-6$ or $2$?

    $2$. Positive numbers are always to the right of negative numbers.

38. Which is true: $| -4 | > | -6 |$ or $-4 > -6$? (Choose the true statement.)

    $-4 > -6$. -4 is to the right of -6 on the number line.

39. Which inequality shows order, not absolute value: $|a| < |b|$ or $a < b$?

    $a < b$. No absolute value bars means comparing positions.

40. Which statement is true: If $|a| < |b|$, then $a < b$ always, sometimes, or never?

    Sometimes. Depends on signs; $|-5| > |3|$ but $-5 < 3$.

41. Choose the correct comparison: Is $|-4|$ greater than, less than, or equal to $|4|$?

    $|-4| = |4|$. Both equal $4$ since absolute value removes sign.

42. Which inequality must be true: If $a<b$, then $|a|<|b|$?

    Not necessarily true. Example: $-5 < 3$ but $|-5| > |3|$.

43. What does the inequality $|a| < |b|$ compare: order on the number line or distance from $0$?

    Distance from $0$ (absolute value), not left-right order. Absolute value bars indicate distance from zero, not position.

44. Identify the correct comparison: $-1$ and $-5$; which has the greater absolute value?

    $-5$. $|-5| = 5 > 1 = |-1|$.

45. What does the inequality $a < b$ state about the order of $a$ and $b$?

    $a$ is to the left of $b$ on the number line. Numbers increase from left to right on the number line.

46. Choose the correct comparison: $-8$ and $5$ (absolute value comparison).

    $|-8| > |5|$. $|-8| = 8$ and $|5| = 5$, so $8 > 5$.

47. Which statement is true: If $a < b$, then $|a| < |b|$ always, sometimes, or never?

    Sometimes. True when both are negative, false when signs differ.

48. Which statement is about order: $-3 < 2$ or $|-3| < |2|$?

    $-3 < 2$. Compares positions on the number line.

49. Which number is greater in order, and which is greater in absolute value: $-9$ or $4$?

    Order: $4$; absolute value: $-9$. $4 > -9$ in order, but $|-9| = 9 > 4$.

50. Which number is farther from $0$: $-6$ or $2$?

    $-6$. $|-6| = 6$ and $|2| = 2$, so -6 is 6 units from zero.

51. Find and correct the error: "Since $-6 < -2$, then $|-6| < |-2|$."

    Correct: $|-6| > |-2|$. Order and absolute value comparisons can differ.

52. Find and correct the false claim: "$-8 > -3$ because $|-8| > |-3|$." What is the correct order statement?

    $-8 < -3$. Absolute value doesn't determine order for negatives.

53. Which absolute value is greater: $|-8|$ or $|5|$?

    $|-8|$. $|-8| = 8$ and $|5| = 5$, so $8 > 5$.

54. Which is farther from $0$: $-4$ or $3$?

    $-4$. $|-4| = 4$ and $|3| = 3$, so $-4$ is farther.

55. What is the absolute value definition in words for $|x|$?

    The distance of $x$ from $0$ on the number line. Absolute value removes the sign, keeping only magnitude.

56. Choose the correct comparison: $-8$ and $5$ (order comparison).

    $-8 < 5$. Negative is less than positive on the number line.

57. What is the absolute value of $-7$, written as $|-7|$?

    $7$. Absolute value removes the negative sign.

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