Download Introduction to Signed Numbers

Introduction to Signed Numbers
Most of the numbers we deal with in our day to day life are larger than zero, or positive
numbers. Sometimes, however, we need to talk about numbers less than zero, or negative
numbers. Let’s use money for an example:
A positive number means you have money.
Use a “+” to show positive or plus
A negative number means you owe money.
Use a “–” to show negative or minus
Zero is neither positive nor negative
Because numbers are naturally positive writing a “+” in front of a number has NO EFFECT.
+7 = 7
++7 = 7
+–7 = –7
–+7 = –7
That means you can “ignore” the “+” sign
But what about the “–” sign?
Think of “–” as meaning OPPOSITE.
Take 4, for example. Now writing “–” will make the line flip to the opposite side of zero.
–4
–6
–4
This is called a number line.
Notice it looks like a
thermometer laying on its side.
+4
–2
0
2
4
6
Opposites are officially defined as the number the same distance from zero but on the
opposite side of zero. For example, the opposite of -7 is +7 and the opposite of 9 is -9.
Now you try: Find the opposites of the following numbers:
The opposite of -3 is _____.
The opposite of -1.2 is _____.
The opposite of ⅕ is _____.
The opposite of 0 is _____.
Absolute Value
The absolute value of a number is its distance from zero regardless of the direction. So
more simply put, the absolute value is the number without its sign (always
made positive). We use two vertical lines to represent absolute value.
Examples:
Now you try:
3  3
9 
2 2
16  16
4 
0 0
 22 
1 
Graphing Signed Numbers
Lets go back to the number line. A number line is a line with equally spaced tick marks
named by numbers. The arrows on the ends of the number line mean that it goes on forever in
both directions.
-6 -5
-4 -3 -2
-1
0
1
2
3
4
5
6
As you can see, all the positive numbers are to the right of zero, and the negative
numbers are to the left of zero. If you want to graph a number on this line, you find the mark
corresponding to the number you wish to graph and put a solid dot there.
For example, graph  3 :
-6
Now you try:
Graph  5
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Graph 2
0
Graph 0
0
Graph  1
0
0
Comparing Signed Numbers
One way of comparing signed numbers is looking at them on the number line. The largest
number is always the number furthest to the right.
Example: compare  4 and  2
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
 2 is furthest to the right so  4  2
So the number the furthest to the right on a number line is the largest number, but an
easier way to think of it is, again, money. Which is more, a +7 in your bank account or a –5 ? Of
course the positive number is always greater. But what about –6 and –9 ? The –6 is greater
since it is better to only owe $6 than to owe $9.
In math we compare numbers using greater than > and less than <
signs. An easy way to remember which one is which is to think of the
greater/less than sign as an alligator head. The alligator always wants to eat
more so he will open his mouth towards the larger number.
Here are some examples:
 28  17
 15  22
0  5
8  12
Now you try: Put a > or a < in the blank to make the statement true:
–8 ____ –5
21 ____ –21
–15 _____ –2
-4 ____-2
0 ____ –11
–102 ____ –120
–3 ____ 2
3 ____ 0
Answers to “Now you try”s
The opposite of -3 is
3
.
The opposite of ⅕ is -⅕ .
9  9
4  4
Graph  5
0
Graph 0
The opposite of -1.2 is
The opposite of 0 is
 22  22
Graph 2
1.2
.
0 .
1 1
0
Graph  1
0
0
–8 < –5
21 > –21
–15 < –2
-4 < -2
0 > –11
–102 > –120
–3 < 2
3> 0