Compare 15 and −20
A hiker stands fifteen feet above sea level. A diver swims twenty feet below. Where do they land on a number line?
Here's our number line. Zero is sea level. Up is positive, down is negative.
The hiker is at positive fifteen — to the right of zero.
The diver is at negative twenty — to the left of zero.
Which number is greater? On a number line, the one farther to the right is always greater.
Fifteen is greater than negative twenty. So the hiker is at the higher position.
But who is farther from sea level? That's a different question — it's about distance from zero.
The absolute value of fifteen is fifteen. The hiker is fifteen feet from sea level.
The absolute value of negative twenty is twenty. The diver is twenty feet from sea level.
Twenty is greater than fifteen. So the diver is actually farther from sea level than the hiker.
Negative twenty is less than fifteen — but its absolute value is bigger. Order and distance from zero are two different ideas!