Absolute Value and the Number Line
Understanding distance from zero and comparing values
Absolute Value and the Number Line
Understanding distance from zero and comparing values
Math - Grade 6-8
- 1
Find the absolute value of -9. Explain what your answer means on a number line.
Absolute value measures distance from 0, and distance is never negative.
The absolute value of -9 is 9. This means -9 is 9 units away from 0 on the number line. - 2
Find the absolute value of 14.
The absolute value of 14 is 14 because 14 is 14 units away from 0. - 3
Write the symbol for the absolute value of -6, then find its value.
Use two vertical bars around the number.
The symbol is |-6|, and its value is 6 because -6 is 6 units from 0. - 4
Plot -4 and 4 on a number line. What do these two numbers have in common?
The numbers -4 and 4 are both 4 units away from 0. They have the same absolute value. - 5
Compare using <, >, or =: |-8| ___ |5|. Explain your choice.
Find each absolute value before comparing.
|-8| is 8 and |5| is 5, so |-8| > |5|. - 6
Compare using <, >, or =: |-3| ___ |3|. Explain your choice.
|-3| is 3 and |3| is 3, so |-3| = |3|. - 7
A diver is 12 feet below sea level. Write the diver's position as an integer and find the absolute value of that integer.
Below sea level is represented by a negative number.
The diver's position is -12 feet. The absolute value is 12, which means the diver is 12 feet from sea level. - 8
A mountain peak is 2,300 feet above sea level. Write the elevation as an integer and find its absolute value.
The elevation is 2,300 feet. The absolute value is 2,300 because the peak is 2,300 feet from sea level. - 9
Find all numbers that have an absolute value of 7.
There are usually two numbers the same distance from 0, one on each side.
The numbers are -7 and 7 because both are 7 units away from 0. - 10
Find all integers x that make this equation true: |x| = 10.
The integers are x = -10 and x = 10 because both numbers are 10 units from 0. - 11
Evaluate the expression: |-15| - |6|.
Find each absolute value first, then subtract.
|-15| - |6| = 15 - 6 = 9. - 12
Evaluate the expression: | -4 | + | -11 |.
|-4| + |-11| = 4 + 11 = 15. - 13
Order these numbers from least to greatest: -2, 5, -7, 0, 3.
Numbers farther left on the number line are smaller.
The numbers from least to greatest are -7, -2, 0, 3, 5. - 14
Order these absolute values from least to greatest: |-9|, |2|, |-4|, |0|.
Convert each expression to its distance from 0 before ordering.
The absolute values are 9, 2, 4, and 0, so the order from least to greatest is |0|, |2|, |-4|, |-9|. - 15
Two students are standing on a number line. Ana is at -6 and Ben is at 2. How far apart are they?
Count the units between the two positions on the number line.
Ana and Ben are 8 units apart because the distance from -6 to 0 is 6 units and the distance from 0 to 2 is 2 units, for a total of 8 units.