2
Absolute value: the distance from zero
Discover Mathematics P6: Term 1, Unit 2, Lessons 4–6
GoalFind the absolute value of a number as its distance from 0 and use the symbol | |.
New words
absolute value · the distance of a number from 0 on the number linedistance · how far one point is from another; never negative| x | · the symbol for the absolute value of x
Explanation
The absolute value of a number is how far it is from 0 on the number line. We write it between two bars: |−7| = 7 and |7| = 7. Both −7 and 7 are 7 steps from 0, so opposites always have the same absolute value: |−a| = |a|. A distance can never be negative, so an absolute value is never negative. The absolute value of 0 is 0. It tells us the size of a number and forgets its sign. A diver at −9 m is 9 m away from the surface, and a loss of 50 LE has an absolute value of 50 LE.
ƒFormula
|−7| = 7 |7| = 7 |0| = 0
Distance from 0 is never negative
Worked examples
Both −7 and 7 are 7 steps from 0. That is why |−7| = 7 and |7| = 7.
| Number | Distance from 0 | Absolute value |
|---|---|---|
| −12 | 12 steps | |−12| = 12 |
| 3.5 | 3.5 steps | |3.5| = 3.5 |
| −3/4 | 3/4 of a step | |−3/4| = 3/4 |
| 0 | 0 steps | |0| = 0 |
| Day | Change (LE) | Absolute value |
|---|---|---|
| Yesterday | −50 | 50 |
| Today | 50 | 50 |
Class activity
Step counting. Stand on the zero of a floor number line. A grown-up calls a number such as −6 or 4.5 (use tape for halves). Walk to it and say how many steps you walked, then say the absolute value in a full sentence: the absolute value of −6 is 6.
Practice
1
Find |−15|.
15.
2
Find |8.2| and |0|.
8.2 and 0.
3
Find |−2/5|.
2/5.
4
Which numbers have an absolute value of 6?
6 and −6, because both are 6 steps from 0.
5
A fish is at −4 m and a bird at 4 m. What is the same about them, and what is different?
Both are 4 m from sea level (the same absolute value), but the fish is below and the bird is above.