When you first learned your numbers, way back in
elementary school, you started with the counting numbers: 1, 2, 3, 4, 5, 6, and so on.
Your number line looked something like this:
Later on, you learned about zero, fractions,
decimals, square roots, and other types of numbers, so your number line started looking something
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 subtraction, because there wasn't enough
"space" on the number line to go back nine units:
You can solve this "space" problem
by using negative numbers. The "whole" numbers start at zero and count off to the right;
these are the positive integers. The negative integers start at zero and count off to the left:
Note the arrowhead on the far right end
of the number line above. That arrow tells you the direction in which the numbers are getting bigger.
In particular, that 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: