Distinguish Absolute Value From Order - 6th Grade Math
Card 1 of 25
Find and correct the error: "Since $-6 < -2$, then $|-6| < |-2|$."
Find and correct the error: "Since $-6 < -2$, then $|-6| < |-2|$."
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Correct: $|-6| > |-2|$. Order and absolute value comparisons can differ.
Correct: $|-6| > |-2|$. Order and absolute value comparisons can differ.
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Which statement is about absolute value: $-3 < 2$ or $|-3| < |2|$?
Which statement is about absolute value: $-3 < 2$ or $|-3| < |2|$?
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$|-3| < |2|$. Compares distances from zero.
$|-3| < |2|$. Compares distances from zero.
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Which inequality must be true: If $a<b$, then $|a|<|b|$?
Which inequality must be true: If $a<b$, then $|a|<|b|$?
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Not necessarily true. Example: $-5 < 3$ but $|-5| > |3|$.
Not necessarily true. Example: $-5 < 3$ but $|-5| > |3|$.
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Choose the correct comparison: $-8$ and $5$ (order comparison).
Choose the correct comparison: $-8$ and $5$ (order comparison).
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$-8 < 5$. Negative is less than positive on the number line.
$-8 < 5$. Negative is less than positive on the number line.
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Choose the correct comparison: $-8$ and $5$ (absolute value comparison).
Choose the correct comparison: $-8$ and $5$ (absolute value comparison).
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$|-8| > |5|$. $|-8| = 8$ and $|5| = 5$, so $8 > 5$.
$|-8| > |5|$. $|-8| = 8$ and $|5| = 5$, so $8 > 5$.
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Which statement matches: "$x$ is closer to $0$ than $y$"?
Which statement matches: "$x$ is closer to $0$ than $y$"?
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$|x| < |y|$. Smaller absolute value means closer to zero.
$|x| < |y|$. Smaller absolute value means closer to zero.
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Which statement matches: "$x$ is to the left of $y$ on the number line"?
Which statement matches: "$x$ is to the left of $y$ on the number line"?
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$x < y$. Left position means smaller value.
$x < y$. Left position means smaller value.
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Which statement is about order: $-3 < 2$ or $|-3| < |2|$?
Which statement is about order: $-3 < 2$ or $|-3| < |2|$?
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$-3 < 2$. Compares positions on the number line.
$-3 < 2$. Compares positions on the number line.
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What does the inequality $|a| < |b|$ compare: order or distance from $0$?
What does the inequality $|a| < |b|$ compare: order or distance from $0$?
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Distance from $0$ (absolute value), not order. Absolute value measures distance, not position.
Distance from $0$ (absolute value), not order. Absolute value measures distance, not position.
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What does the inequality $a < b$ state about the order of $a$ and $b$?
What does the inequality $a < b$ state about the order of $a$ and $b$?
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$a$ is to the left of $b$ on the number line. Numbers increase from left to right on the number line.
$a$ is to the left of $b$ on the number line. Numbers increase from left to right on the number line.
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Which absolute value is greater: $|-7|$ or $|-2|$?
Which absolute value is greater: $|-7|$ or $|-2|$?
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$|-7|$. $|-7| = 7$ and $|-2| = 2$, so $7 > 2$.
$|-7|$. $|-7| = 7$ and $|-2| = 2$, so $7 > 2$.
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Choose the true statement: $-5 < -1$ or $|-5| < |-1|$?
Choose the true statement: $-5 < -1$ or $|-5| < |-1|$?
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$|-5| < |-1|$ is false; $|-5| > |-1|$ is true. $|-5| = 5$ and $|-1| = 1$, so $5 > 1$.
$|-5| < |-1|$ is false; $|-5| > |-1|$ is true. $|-5| = 5$ and $|-1| = 1$, so $5 > 1$.
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Which number is greater: $-7$ or $-2$?
Which number is greater: $-7$ or $-2$?
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$-2$. On the number line, $-2$ is to the right of $-7$.
$-2$. On the number line, $-2$ is to the right of $-7$.
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Identify the correct conclusion: If $|a| = |b|$, what can be true about $a$ and $b$?
Identify the correct conclusion: If $|a| = |b|$, what can be true about $a$ and $b$?
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$a=b$ or $a=-b$. Equal distances can be in opposite directions.
$a=b$ or $a=-b$. Equal distances can be in opposite directions.
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What is the absolute value definition in words for $|x|$?
What is the absolute value definition in words for $|x|$?
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The distance of $x$ from $0$ on the number line. Absolute value removes the sign, keeping only magnitude.
The distance of $x$ from $0$ on the number line. Absolute value removes the sign, keeping only magnitude.
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Which is farther from $0$: $-4$ or $3$?
Which is farther from $0$: $-4$ or $3$?
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$-4$. $|-4| = 4$ and $|3| = 3$, so $-4$ is farther.
$-4$. $|-4| = 4$ and $|3| = 3$, so $-4$ is farther.
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Which is greater: $-4$ or $3$?
Which is greater: $-4$ or $3$?
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$3$. Positive numbers are always greater than negative numbers.
$3$. Positive numbers are always greater than negative numbers.
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Identify the correct statement: If $a<0$, what is $|a|$ equal to?
Identify the correct statement: If $a<0$, what is $|a|$ equal to?
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$|a|=-a$. For negative numbers, absolute value equals the opposite.
$|a|=-a$. For negative numbers, absolute value equals the opposite.
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Choose the correct comparison: Is $|-4|$ greater than, less than, or equal to $|4|$?
Choose the correct comparison: Is $|-4|$ greater than, less than, or equal to $|4|$?
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$|-4| = |4|$. Both equal $4$ since absolute value removes sign.
$|-4| = |4|$. Both equal $4$ since absolute value removes sign.
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What does the statement $|a| > |b|$ compare: location on the number line or distance from $0$?
What does the statement $|a| > |b|$ compare: location on the number line or distance from $0$?
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Distance from $0$ (magnitude), not left-right order. Absolute value measures how far from zero, not position.
Distance from $0$ (magnitude), not left-right order. Absolute value measures how far from zero, not position.
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What does the statement $a > b$ describe: distance from $0$ or position (order) on the number line?
What does the statement $a > b$ describe: distance from $0$ or position (order) on the number line?
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Position (order): $a$ is to the right of $b$. Order compares positions on the number line.
Position (order): $a$ is to the right of $b$. Order compares positions on the number line.
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Which inequality shows order, not absolute value: $|a| < |b|$ or $a < b$?
Which inequality shows order, not absolute value: $|a| < |b|$ or $a < b$?
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$a < b$. No absolute value bars means comparing positions.
$a < b$. No absolute value bars means comparing positions.
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Which inequality compares distances from $0$: $|a| < |b|$ or $a < b$?
Which inequality compares distances from $0$: $|a| < |b|$ or $a < b$?
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$|a| < |b|$. Absolute value bars compare distances from zero.
$|a| < |b|$. Absolute value bars compare distances from zero.
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What is the absolute value of $-7$, written as $|-7|$?
What is the absolute value of $-7$, written as $|-7|$?
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$7$. Absolute value removes the negative sign.
$7$. Absolute value removes the negative sign.
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Which number is greater: $-3$ or $2$?
Which number is greater: $-3$ or $2$?
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$2$. Positive numbers are always greater than negatives.
$2$. Positive numbers are always greater than negatives.
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