6th Grade Math Flashcards: Understand Absolute Value Concept

What this deck covers

This deck focuses on Understand Absolute Value Concept, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the absolute value $|-2.5|$?

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

Flashcard 2: What is the value of $|-0.2|$?

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

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

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

Flashcard 4: What is the value of |-
.5|?

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

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

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

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

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

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

Answer: $45. Debt magnitude is the positive amount owed.

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

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

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

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

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

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

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

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

Flashcard 12: What is $|a|$ if $a$ is a nonnegative rational number?

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

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

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

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

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

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

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

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

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

Flashcard 17: What is the absolute value $|0|$?

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

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

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

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

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

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

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

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

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

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

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

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

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

Flashcard 24: What is the absolute value $|7|$?

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

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

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

Flashcard 26: What is the value of $|0|$?

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

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

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

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

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

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

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

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

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

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

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

Flashcard 32: What is the value of $|-7|$?

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

Flashcard 33: What is the value of $|7|$?

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

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

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

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

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

Flashcard 36: What is $|a|$ if $a$ is a negative rational number?

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

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

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

Flashcard 38: What is the absolute value $|-7|$?

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

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

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

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

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