Compare absolute values

In grade 6 you learned that the absolute value `|x|` means the distance of the number from zero. So it is always non-negative.

In grade 7 we go further and compare two absolute values with each other. It is intuitive, but easy to slip up if you confuse the original numbers with their absolute values.

Example

`|−5|` ? `|3|`

First compute the absolute values:

• `|−5| = 5` (distance of −5 from zero).
• `|3| = 3`.

Now compare: `5 > 3`, so `|−5| > |3|`. Even though −5 < 3.

Where is the trap?

Negative numbers sit "to the left" of zero on the number line. `−5` is farther from zero than `3`, even if it is "smaller" in the usual ordering.

Rule: when comparing absolute values, ignore the signs — only look at the distance from zero.

Tips

• Compute `|a|` and `|b|` separately, then compare.
• Turn a negative into a positive in your head: `|−5|` is just `5`.
• Very typical case: one number positive, the other negative. The positive often "loses" if the negative is far from zero.

Typical problems

Try it yourself

• Compare absolute values
• Absolute value and opposite number
• Negative numbers on a number line