Order Rational Numbers in Context - 6th Grade Math

1. What does the statement $4 > -2$ mean about which value is greater?

   $4$ is greater than $-2$. Positive numbers are always greater than negative numbers.

2. Identify the correct order from least to greatest: $-2,\ 0,\ -5,\ 3$.

   $-5,\ -2,\ 0,\ 3$. Arrange from most negative to most positive.

3. What is the correct order from greatest to least: $-1.2,\ -1.05,\ -1.5$?

   $-1.05 > -1.2 > -1.5$. Order negatives by comparing distances from zero.

4. What does the statement $x > 0$ mean if $x$ represents profit in dollars?

   There is a profit (a positive amount). Positive values indicate gains or increases.

5. Which number is closest to $0$: $-0.3$ or $0.25$?

   $0.25$. $0.25$ is $0.25$ units from zero; $-0.3$ is $0.3$ units away.

6. What is the correct inequality for "an elevation of $-12$ m is below $-5$ m"?

   $-12 < -5$. Lower elevations have smaller numerical values.

7. Choose the word that makes this true: $-8$ is ____ $-2$ (less than or greater than).

   less than. For negative numbers, larger absolute value means smaller number.

8. Which temperature is colder: $-12^\circ\text{C}$ or $-7^\circ\text{C}$?

   $-12^\circ\text{C}$. Lower temperatures have more negative values.

9. Identify the correct order from greatest to least: $\frac{1}{2},\ -\frac{3}{4},\ 0,\ 1$.

   $1,\ \frac{1}{2},\ 0,\ -\frac{3}{4}$. Arrange from most positive to most negative.

10. What does the inequality $5 > -1$ state about the order of these numbers?

    $5$ is greater than $-1$. Positive numbers are always greater than negative numbers.

11. Which number is greater: $0$ or $-\frac{1}{8}$?

    $0$. Zero is greater than any negative number.

12. What is the correct order from least to greatest: $-2,\ 0,\ -5,\ 3$?

    $-5 < -2 < 0 < 3$. Negative numbers come before zero, then positive numbers.

13. What is the correct inequality for "$5$ degrees is warmer than $-1$ degrees"?

    $5 > -1$. Higher temperatures are represented by greater numbers.

14. Choose the correct symbol: a balance of -$12 $ \square $ a balance of -$20$.

    $>$. Owing -$12 is better than owing -$20 (less debt).

15. Which symbol makes this statement true: $-9\ \square\ -2$ if $-9$ is smaller?

    $<$. $-9$ is farther from zero than $-2$ on the number line.

16. Which symbol makes this statement true: $\frac{1}{4} \square \frac{3}{8}$?

    $<$. $\frac{1}{4} = 0.25$ and $\frac{3}{8} = 0.375$, so $\frac{1}{4}$ is smaller.

17. What does "closest to $0$" mean on a number line for rational numbers?

    It has the smallest distance from $0$. The number with the smallest absolute value is closest.

18. Identify the correct comparison for debts: owing $-\$20$ versus owing $-\$35$.

    $-20 > -35$. Owing $20 is better than owing $35, so $-20 > -35$.

19. Which symbol makes this statement true: $-4\ \square\ -7$ if $-4$ is greater?

    $>$. $-4$ is closer to zero than $-7$ on the number line.

20. Which number is greater: $-\frac{3}{4}$ or $-\frac{2}{3}$?

    $-\frac{2}{3}$. $-\frac{2}{3} \approx -0.67$ is closer to zero than $-\frac{3}{4} = -0.75$.

21. Which number is greater: $-2.6$ or $-2.06$?

    $-2.06$. For negative numbers, the one closer to zero is greater.

22. What does the statement $0 > -0.03$ mean in a money context?

    $0 is more money than owing $0.03. Having zero dollars is better than owing money (negative balance).

23. What is the correct comparison: $-0.6\ \square\ -0.59$?

    $-0.6 < -0.59$. $-0.6 = -0.60$, which is less than $-0.59$.

24. Which is greater: $-\frac{5}{6}$ or $-\frac{1}{2}$?

    $-\frac{1}{2}$. $-\frac{1}{2} = -0.5$ is closer to zero than $-\frac{5}{6} \approx -0.83$.

25. Which number is greatest: $-\frac{3}{5}$, $-0.62$, or $-0.6$?

    $-0.6$. $-\frac{3}{5} = -0.6$, which is closer to zero than $-0.62$.

26. Find the correct symbol: $-\frac{7}{8} \square -0.9$.

    $>$ $-\frac{7}{8} = -0.875$, which is greater than $-0.9$.

27. What is the correct order from greatest to least: $\frac{-1}{2}$, $\frac{2}{3}$, $-0.4$?

    $\frac{2}{3} > -0.4 > \frac{-1}{2}$. Positive numbers are greatest, then negatives closer to zero.

28. Find and correct the false statement: "Since $-4$ is left of $-1$, $-4 > -1$."

    Correct: $-4 < -1$. Numbers to the left are less than, not greater than.

29. Which elevation is higher: $-15$ meters or $8$ meters (relative to sea level)?

    $8$ meters. Positive elevations are above sea level, higher than negative ones.

30. What does the inequality $-3 < 2$ state about the order of these numbers?

    $-3$ is less than $2$. Negative numbers are always less than positive numbers.

31. Which elevation is higher: $-15\text{ m}$ or $-40\text{ m}$ (relative to sea level $0\text{ m}$)?

    $-15\text{ m}$. $-15$ is closer to sea level than $-40$.

32. Which number represents the lower temperature: $-9^\circ\text{C}$ or $-2^\circ\text{C}$?

    $-9^\circ\text{C}$. Lower temperatures have smaller numerical values.

33. What does it mean if a bank balance changes from $-12$ dollars to $-5$ dollars?

    The balance increased because $-5 > -12$. Moving from $-12$ to $-5$ means less debt, which is an increase.

34. Which number is less: $\frac{-5}{6}$ or $\frac{-3}{4}$?

    $\frac{-5}{6}$. $\frac{-5}{6} \approx -0.83$ and $\frac{-3}{4} = -0.75$, so $\frac{-5}{6}$ is less.

35. Which inequality correctly represents: "$-3$ is at least $-3$"?

    $-3 \ge -3$. "At least" means greater than or equal to.

36. Which statement is correct for distances: $-3$ km (west) compared to $2$ km (east)?

    $-3 < 2$. West (negative) is less than east (positive) on a number line.

37. What is the correct order from least to greatest: $-1$, $0.2$, $-0.8$?

    $-1 < -0.8 < 0.2$. Negative numbers increase as they approach zero, then positive numbers.

38. A bank account has balances $-\$25$ and $10. Which balance is greater?

    $10. Positive balance is greater than negative debt.

39. What does $-8^\circ\text{C} < -3^\circ\text{C}$ mean about the temperatures?

    $-8^\circ\text{C}$ is colder than $-3^\circ\text{C}$. Lower negative temperatures indicate colder conditions.

40. Which symbol makes this statement true: $-7 \square -9$ if $-7$ is greater than $-9$?

    $>$. Since $-7$ is closer to zero than $-9$, it's the larger value.

41. Identify the correct statement: Is $-\frac{3}{2}$ less than or greater than $-1$?

    $-\frac{3}{2} < -1$. $-\frac{3}{2} = -1.5$, which is less than $-1$.

42. Identify the number closest to $0$: $-0.9,\ 0.2,\ -0.1$.

    $-0.1$. $|-0.1| = 0.1$ is the smallest absolute value.

43. Identify the greater number: $-0.6$ or $-0.4$.

    $-0.4$. Among negatives, the number closer to zero is greater.

44. Which symbol makes this true: $\frac{1}{4} \square \frac{3}{8}$?

    $<$. $\frac{1}{4} = \frac{2}{8}$, which is less than $\frac{3}{8}$.

45. Choose the correct statement: If $a$ is to the left of $b$ on a number line, then $a\ \square\ b$.

    $a < b$. Numbers increase from left to right on a number line.

46. Which inequality matches "at most $-2$ degrees": temperature $T$ is no greater than $-2$?

    $T \le -2$. "At most" means less than or equal to the given value.

47. What does "$A$ is at $-15$ ft and $B$ is at $-6$ ft; $A < B$" mean in context?

    $A$ is lower (deeper) than $B$. Smaller negative values represent deeper positions below sea level.

48. What does the inequality $4.2 > -0.5$ mean in a real-world comparison?

    $4.2$ represents a greater value than $-0.5$. Positive numbers are always greater than negative numbers.

49. A diver is at $-6\text{ m}$ and then at $-9\text{ m}$. Which position is deeper?

    $-9\text{ m}$. More negative depth means farther below surface.

50. What does the statement $x < 0$ mean if $x$ represents a change in temperature?

    The temperature decreased (a negative change). Negative values represent decreases or drops.

51. Which inequality matches "a depth of $-30$ m is deeper than $-18$ m"?

    $-30 < -18$. Deeper depths have more negative (smaller) values.

52. Find and correct the false statement: $-\frac{1}{2} > \frac{1}{4}$.

    $-\frac{1}{2} < \frac{1}{4}$. Negative fractions are less than positive fractions.

53. What does the statement $-3 < -1$ mean in terms of position on a number line?

    $-3$ is to the left of $-1$. On a number line, smaller numbers are positioned to the left.

54. What is the meaning of ordering rational numbers from least to greatest on a number line?

    Left to right: smallest to largest. Numbers increase as you move right on the number line.

55. What does the inequality $-3 < -1$ mean in terms of position on a number line?

    $-3$ is to the left of $-1$. On a number line, smaller numbers are positioned to the left of larger numbers.

56. Which is deeper below sea level: $-32$ meters or $-27$ meters?

    $-32$ meters. More negative values represent greater depths below sea level.

57. Which inequality correctly represents: "$-2$ is no more than $5$"?

    $-2 \le 5$. "No more than" means less than or equal to.

58. Which number is less: $-1.2$ or $-1.05$?

    $-1.2$. $-1.2$ is farther from zero than $-1.05$.

59. Which symbol makes this true: $-7\ \square\ -9$ if $-7$ is greater than $-9$?

    $>$. For negative numbers, the one closer to zero is greater.

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