When you first learned
your numbers, way back in elementary school, you learned the counting
number: 1,
2, 3, 4, 5, 6, and
so on. Your number line looked like this:
Later on, you
learned about zero, fractions, decimals, square roots, and other types
of numbers, so your number line started looking something like this:
Addition, multiplication,
and division always made sense --as long as you didn't try to divide by
zero-- but sometimes subtraction didn't work. If you had "9
– 5", you got
4:
But what if you
had "5
– 9"? You just
couldn't do this, because there wasn't enough "space":
You can solve
this "space" problem by using negative numbers. The "whole"
numbers start at zero and count off to the right. The negatives start
at zero and count off to the left:
Note the arrowhead
on the far right end of the number line. The arrow tells you the direction
in which the numbers are getting bigger. Then the arrow also tells you
that the negatives are getting smaller as they move off to the
left. That is, –5
is smaller than –4.
This might seem a bit
weird at first, but that's okay; negatives take some getting used to.
Let's look at a few inequalities, to practice your understanding. Refer
to the number line above, as necessary.
Complete the following
inequality: 3
_____ 6
Look at the number line:
Since 6 is
to the right of 3,
then 6 is
larger, so the correct inequality is:
Look at the number line:
Since –6 is
to the left of –3,
then –3,
being further to the right, is actually the larger number. So the
correct inequality is:
