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Integers
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The number line
...
-10
-9 -8 -7 -6
-5 -4 -3 -2 -1
1
2
3
4
5
6
7
8
9
10
...
0
Signed Numbers
Think about what happens with you subtract 5 from 2. Your first reaction might be “you can‟t take
five away from two!!” and in a way, you‟re right. Previously, we were only looking at numbers that
are positive, but numbers can also be negative! The number line above shows that when a number
drops below „0‟, it becomes negative. For negative numbers, the lower a negative number gets, the
greater a value it has. For instance, -5 is a higher than -10 because it is closer to 0. This is somewhat
counter-intuitive because, when thinking about positive numbers, you may think that 10 is twice as
large as 5 because it is twice as far away from 0. An easy way to remember is that the further right on
the number line, the higher the number, and the further left, the lower the number.
All integers have two distinguishing attributes that allow mathematicians to specify where a number
is on the number line. These two attributes are the magnitude, and the sign.
Magnitude
The magnitude of an integer is a measure of how large it is. The magnitude is represented by
the actual number itself, and represents how far away it is from the number „0.‟ As an
example, the number 7 has a magnitude of „7‟, which means that it is seven units away from
zero on the number line. The number -5 has a magnitude of „5‟ because it is five units away
from zero.
Sign
The sign of an integer is either „−‟ (negative) or „+‟ (positive), which shows whether the
number is to the left or right of „0‟ on the number line. If the number is negative, then it can
be found to the left of „0‟, and if the number is positive it will be on the right side of „0.‟
Typically, when dealing with a positive number, the „+‟ sign is left out to avoid confusion.
Subtracting with negative results
When you subtract a positive number from a positive number, the result is moving that many
places to the left along the number line. Think of the number line as a thermometer. What
happens if you are at 2°C and the temperature drops 5°? You end up at 3° below zero or
−3°C. So, 2 − 5 = −3.
The set of integers includes all whole numbers including positive and negative numbers and
zero (which is neither positive nor negative). Thus, the set of integers includes all the whole
numbers on the number line.
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905.721.2000 ext. 2491
This document last updated: 12/22/2010
Student Academic Learning Services
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Adding Negative Numbers
When you add a number to another number, you are moving so many spaces along the
number line. The magnitude of the number tells you how many spaces and the sign of the
number tells you the direction to move in. If the number you are adding is positive then you
move to the right. If it is negative, you move to the left.
Start from five and move three places left
Start from negative two and move 4 places left
Subtracting Negative Numbers
When you subtract any number from another, you move that many spaces on the number line
in the opposite direction. Thus, when you subtract a positive number, you move to the left.
However, when you subtract a negative number, you move to the right. (Since you are
moving to the right you can think of subtracting a negative number as being the same thing
as adding that number as a positive.)
Start from four and move 6 places right
Star from negative two and move five places right
Multiplying and Dividing with Negative Numbers
To find the magnitude of the answer, simply multiply or divide as you would if both numbers
were positive.
To find the sign of the answer, use the following table:
You can use exactly the same table with division in place of multiplication. Examples:
Expressions with Integers
www.durhamcollege.ca/sals
Student Services Building (SSB), Room 204
905.721.2000 ext. 2491
This document last updated: 12/22/2010