Absolute value as distance from zero

Mathematics · Number Representation & Place Value · ages 11-12

Name ______________________ Date ____________

What is the absolute value of -7?
Answer: ______________
What does the absolute value of a number tell you?
- How far the number is from zero
- The sign of the number, positive or negative
- How many digits the number has
The absolute value of a number can be negative.
Circle one: True False
What is the absolute value of -12?
Answer: ______________
What is |4.5|?
- 4.5
- -4.5
- 0
A submarine sits at -45 meters (45 meters below sea level). A drone flies at 30 meters above sea level. Which one is farther from sea level?
- The submarine, since |-45| = 45 is greater than |30| = 30
- The drone, since 30 is a positive number
- They are the same distance from sea level
Maria owes $18, written as -18. She has $12 in savings, written as +12. Which amount has the greater absolute value?
- -18, because |-18| = 18 is greater than |12| = 12
- +12, because it is a positive number
- They are equal
Amir says: since -8 is less than -3, the absolute value of -8 must also be less than the absolute value of -3. Is Amir correct?
- No, because |-8| = 8 is greater than |-3| = 3
- Yes, that's correct
- No, because both absolute values are equal

Answer key

For grown-ups. Fold this page away before handing over the rest.

7 · -7 is 7 steps from zero, so its absolute value is 7.
How far the number is from zero · Absolute value is a distance. It tells you how many steps the number is from zero, not its sign or size in digits.
False · Absolute value is a distance, and a distance is never negative. It's always zero or positive.
12 · -12 is 12 steps from zero, so |-12| = 12.
4.5 · 4.5 is already positive, and it's 4.5 steps from zero, so its absolute value stays 4.5.
The submarine, since |-45| = 45 is greater than |30| = 30 · Distance from sea level is an absolute value question. 45 is farther than 30, no matter that the submarine's number is negative.
-18, because |-18| = 18 is greater than |12| = 12 · The size of the debt, 18, is bigger than the savings, 12, once you compare distances from zero instead of the signs.
No, because |-8| = 8 is greater than |-3| = 3 · Ordering signed numbers and ordering their absolute values can point in opposite directions. -8 is the smaller number, but 8 is the bigger distance.