AI Tutor
If you take five steps backward, you didn't travel negative five steps — you still walked a physical distance of five steps.
In mathematics, we use absolute value to measure this exact idea: the size or distance of a number, completely ignoring its direction.

Distance from Zero

The absolute value of a real number xx, written with two vertical bars as ∣x∣|x|, is its distance from zero on a number line.
In 1841, German mathematician Karl Weierstrass introduced these vertical bars as a clean way to write the size of a quantity without worrying about its sign.
Because distance is always zero or positive, ∣x∣≥0|x| \ge 0 for every real number xx.
What happens when an expression sits inside those vertical bars? Let's look at how absolute value fits into the order of operations.

Absolute Value as a Grouping Symbol

Absolute value bars act just like parentheses in the order of operations: you must completely simplify the inside first before applying the absolute value.
Once you evaluate the inside to a single number, turn that number into its non-negative distance value, and then continue with any multiplication, addition, or subtraction outside.
A common mistake is turning every minus sign inside the bars into a plus sign before subtracting — like writing ∣3−8∣|3 - 8| as 3+8=113 + 8 = 11.