Absolute value measures distance — and distance is always positive. This skill shows up in GED problems about elevation, temperature, money, and direction. Learn to recognize it even when the words "absolute value" never appear.
Absolute value answers one question: how far? It tells you the distance between two numbers on a number line — and distance is always a positive number, no matter which direction you go.
The absolute value bars look like this: | | Whatever is inside gets its distance from zero. So |−7| = 7 because −7 is 7 steps from zero. And |7| = 7 for the same reason — just in the other direction.
When you need the distance between two numbers, you can subtract them in either order — as long as you put the whole expression inside absolute value bars. Both expressions are correct and give the same answer.
What is the distance between −3 and 5 on a number line?
Both expressions give 8. The GED may ask you to pick the correct expression — not calculate the answer. Know that both forms are valid.
In everyday life, we almost never say "negative." We say below, under, down, behind, in debt, lower than. The direction is built into the word — but the distance is just the number.
If one person is 25 and another is 31, we say they are 6 years apart — not "positive 6" or "negative 6." The absolute value gives us that plain number.
Same with directions. We don't say "negative 4 blocks." We say 4 blocks east, 4 blocks back, 4 feet below sea level. The word tells the direction. The absolute value gives the distance.
A hiker is at 340 feet above sea level. A submarine is 85 feet below sea level. What is the distance between their elevations?
The temperature on Monday was −4°F. On Tuesday it was 17°F. How many degrees did the temperature change?
Absolute value = distance. Distance is always positive. To find the distance between two numbers, subtract them in either order and put the result inside absolute value bars. On the GED, this skill hides inside problems about elevation, temperature, money, direction, and floors in a building. Watch for words like below, beneath, under, down, in debt, lower than — those signal a negative number.