Writing numbers down on a Number Line makes it easy to tell
which numbers are bigger or smaller.
|Negative Numbers (−)||Positive Numbers (+)|
|(The line continues left and right forever.)|
A number on the left is smaller than a number on the right.
- 5 is smaller than 8
- −1 is smaller than 1
- −8 is smaller than −5
A number on the right is larger than a number on the left.
- 8 is larger than 5
- 1 is larger than −1
- −5 is larger than −8
Try this interactive number line (click to mark):
You can also try the zoomable number line.
- John borrowed $3 to pay for his lunch
- Virginia borrowed $5 to pay for her lunch
- Alex had enough money for lunch and has $3 left over
Place these people on the number line to find who is poorest and who is richest.
Owing money is negative
Having money is positive
So John has "−3", Virginia has "−5" and Alex has "+3"
Now it is easy to see that:
Virginia is poorer than John (−5 is less than −3)
and John is poorer than Alex (−3 is smaller than 3)
and Alex is, of course, the richest!
Using The Number Line
We can use the number line to help us add. We always move to the right to add.
We can use the number line to help us subtract. We always move to the left to subtract.
Absolute Value means to think only about how far a number is from zero.
For example "6" is 6 away from zero, but "−6" is also 6 away from zero.
So the absolute value of 6 is 6, and the absolute value of −6 is also 6