Prairie Minds
MATH · GRADE 7Number

Absolute Value: How Far From Zero

How far from zero, no matter which way.

Grade 7
04 units4 units−4+4|−4| = |+4| = 4

What is absolute value?

The absolute value of a number is its distance from zero on the number line. Distance is never negative — it doesn't matter which direction you travel.

We write it with two upright bars:

∣x∣|x| reads "the absolute value of xx" and means the distance from xx to 0.

Three quick examples:

∣3∣=3|3| = 3 ∣−3∣=3|-3| = 3 ∣0∣=0|0| = 0

The negative sign disappears, because distance is never negative. You can't be "−5 metres away" from something — you're 5 metres away.

See it on the number line

Drag the marker along the line. The orange bar shows the absolute value: how far the point is from zero, regardless of side.

Try it

Drag the marker — see its distance from zero.

|3|=3
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10

Click anywhere on the line to place the marker.

A few things to notice while you play:

  • The bar always starts at 0.
  • It never points "backwards" — it always shows a positive distance, even when the point is on the left side.
  • A point at −7 and a point at +7 give the same distance. The side doesn't matter; only how far.

Where it shows up in real life

A Calgary chinook. Some Calgary mornings start at −25°C. Then a chinook rolls in over the Rockies, and by mid-afternoon the temperature is +12°C — a swing of ∣−25−12∣=37|{-25} - 12| = 37 degrees. The absolute value tells us how big the change was, regardless of which direction it went.

Elevation across Alberta. Banff townsite sits around 1,400 m above sea level. The lowest point in Alberta — the Slave River as it leaves the province — is around 150 m. If you're asking "how much higher is Banff than the lowest point in Alberta?", you want the distance between those two elevations, not a signed difference.

Errors and tolerances. A machinist cutting a 10 cm bolt to a tolerance of ±0.05\pm 0.05 cm doesn't care whether the finished bolt is 0.04 cm too long or 0.04 cm too short — they care that the absolute error stays under 0.05.

Worksheet

These aren't graded. Get them right, get them wrong — the goal is to feel out where the idea works.

Question 1 of 3

Try it

What is |−12.5|?

Multiple choice: what is the absolute value of negative twelve point five? Four answer cards: minus twelve point five, twelve point five, twenty-five, zero.

Going further

Absolute value works the same way for fractions:

∣−34∣=34\left|-\frac{3}{4}\right| = \frac{3}{4}

And for decimals:

∣−0.7∣=0.7|-0.7| = 0.7

The number line above moves in steps of 0.1 — drag it to −0.7 or +0.7 and watch the readout. Different signs, same distance.

Distance from zero comes back beyond integers: measuring the sides of a right triangle with the Pythagorean theorem, describing the spread of data with the interquartile range. Same idea, different settings.