Absolute value
This Grade 6 math skill from Pengi Math (Grade 6) introduces the concept of absolute value. Students learn that the absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. For example, |−5| = 5 and |5| = 5.
Key Concepts
Property The absolute value of $x$ is defined by $$|x| = \begin{cases} x & \text{if } x \geq 0 \\ x & \text{if } x < 0 \end{cases}$$ Absolute value bars act like grouping devices in the order of operations: you should complete any operations that appear inside absolute value bars before you compute the absolute value.
Examples To evaluate $| 9|$, since $ 9 < 0$, we use the second case of the definition: $| 9| = ( 9) = 9$.
To evaluate the expression $10 |5 8|$, first compute the operation inside the absolute value bars: $5 8 = 3$. Then take the absolute value: $| 3| = 3$. Finally, subtract: $10 3 = 7$.
Common Questions
What is absolute value?
Absolute value is the distance of a number from zero on the number line. It is always non-negative. Written with bars: |−7| = 7 and |7| = 7.
How do you find the absolute value of a negative number?
Remove the negative sign. The absolute value of any negative number is the same number made positive, because distance is always positive.
What is the absolute value of zero?
The absolute value of zero is zero, because zero is zero distance from itself.
How is absolute value used in real life?
Absolute value is used to describe distances, differences in temperatures, and magnitudes where direction does not matter—only the size of the quantity.
Where is absolute value taught in Grade 6?
Absolute value is introduced in the Grade 6 Pengi Math textbook as part of the study of integers and the number line.