Understand Absolute Value Concept - 6th Grade Math

1. What is the absolute value $|-2.5|$?

   $2.5$. The distance from $0$ to $-2.5$ is $2.5$ units.

2. What is the value of $|-0.2|$?

   $0.2$. Decimal distances are positive regardless of sign.

3. What does $|-12|$ represent if $-12$ is a temperature change in degrees?

   A change of $12$ degrees (magnitude). Absolute value shows size of change, ignoring direction.

4. What is the value of $|-.5|$?

   $1.5$. Distance is always positive, so drop the negative sign.

5. What is the distance between $-2.5$ and $1.5$ on the number line?

   $4$. Distance is $|-2.5-1.5| = |-4| = 4$.

6. What does the absolute value $|x|$ represent on a number line?

   The distance from $0$ to $x$. Absolute value measures how far a number is from zero.

7. What is the magnitude of a debt of $-\$45$ using absolute value?

   $45. Debt magnitude is the positive amount owed.

8. What are the two numbers that have absolute value $5$?

   $5$ and $-5$. Two numbers equidistant from zero: one positive, one negative.

9. If $|x|=0$, what is the value of $x$?

   $x=0$. Only zero has distance zero from itself.

10. What is the absolute value $\left|-\frac{3}{4}\right|$?

    $\frac{3}{4}$. Absolute value removes the negative sign from any number.

11. What is the distance between $-3$ and $5$ on the number line (use absolute value)?

    $|-3-5|=8$. Distance between points is $|a-b|$; here $|-3-5|=|-8|=8$.

12. What is $|a|$ if $a$ is a nonnegative rational number?

    $|a|=a$. Zero and positive numbers equal their absolute value.

13. A diver is $-12$ meters below sea level. What is the diver's distance from sea level?

    $| -12 |=12$ meters. Distance ignores direction; $12$ meters from sea level.

14. What is the distance between $-3$ and $4$ on the number line?

    $7$. Count units: $|-3-4| = |-7| = 7$.

15. Identify all rational solutions to $|x|=\frac{1}{2}$.

    $x=\frac{1}{2}$ or $x=-\frac{1}{2}$. Two numbers are $\frac{1}{2}$ units from zero.

16. Which expression gives the distance between two numbers $a$ and $b$ on a number line?

    $|a-b|$. Subtract positions and take absolute value for distance.

17. What is the absolute value $|0|$?

    $0$. Zero is at distance zero from itself on the number line.

18. What does the absolute value $|r|$ represent on a number line for any rational number $r$?

    The distance from $0$ to $r$ on the number line. Absolute value measures how far a number is from zero, regardless of direction.

19. If $|x|=\frac{2}{3}$, what are the possible values of $x$?

    $x=\frac{2}{3}$ or $x=-\frac{2}{3}$. Numbers at distance $\frac{2}{3}$ from zero in both directions.

20. What is the distance between $-\frac{1}{2}$ and $\frac{3}{2}$ on the number line?

    $\left|-\frac{1}{2}-\frac{3}{2}\right|=2$. Distance is $\left|-\frac{1}{2}-\frac{3}{2}\right|=|-2|=2$.

21. Identify the value of $x$ if $|x|=6$ and $x$ is negative.

    $x=-6$. Only negative $x$ with distance $6$ from zero is $-6$.

22. A bank account balance is $-\$25$. What does the absolute value represent?

    The magnitude of the debt is $| -25 |=\$25$. Absolute value shows the size of the debt without the negative.

23. What is the value of $| -10 | - | 3 |$?

    $7$. $|-10|=10$ and $|3|=3$, so $10-3=7$.

24. What is the absolute value $|7|$?

    $7$. Positive numbers remain unchanged when taking absolute value.

25. What is the value of $\left|\frac{5}{6}\right|$?

    $\frac{5}{6}$. Positive fractions remain unchanged by absolute value.

26. What is the value of $|0|$?

    $0$. Zero is zero units away from itself.

27. What is always true about the sign of an absolute value $|r|$ for any rational number $r$?

    $|r| \ge 0$ always. Distance is never negative, so absolute values are always non-negative.

28. What is the distance from $0$ to $-9$ on the number line?

    $9$. Distance ignores direction, so $|-9| = 9$.

29. The temperature is $-8^\circ\text{C}$. What is the magnitude of the temperature relative to $0^\circ\text{C}$?

    $|-8|=8^\circ\text{C}$. Magnitude is the size without considering positive/negative.

30. What is the depth magnitude if a diver is at $-18$ meters relative to sea level?

    $18$ meters. Depth magnitude is distance below surface level.

31. Which number has the greater absolute value: $-\frac{7}{8}$ or $\frac{3}{4}$?

    $-\frac{7}{8}$. $\left|-\frac{7}{8}\right|=\frac{7}{8}$ and $\left|\frac{3}{4}\right|=\frac{6}{8}$, so $-\frac{7}{8}$ is greater.

32. What is the value of $|-7|$?

    $7$. Negative numbers become positive when finding distance from zero.

33. What is the value of $|7|$?

    $7$. Positive numbers are already their distance from zero.

34. Identify the correct comparison: $|-6|$ __ $|4|$.

    $|-6|>|4|$. $|-6|=6$ and $|4|=4$, so $6>4$.

35. What is the value of $\left|\frac{-3}{4}\right|$?

    $\frac{3}{4}$. Absolute value removes the negative sign from fractions.

36. What is $|a|$ if $a$ is a negative rational number?

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

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

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

38. What is the absolute value $|-7|$?

    $7$. Negative numbers lose their sign when taking absolute value.

39. What is the absolute value $\left|\frac{5}{6}\right|$?

    $\frac{5}{6}$. Positive fractions stay the same when taking absolute value.

40. Which statement is always true for any rational number $x$: $|x|\ge 0$ or $|x|\le 0$?

    $|x|\ge 0$. Distance is never negative, always zero or positive.

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