Integers
Basically, integers are used to represent situations that whole numbers are not able to represent mathematically.
For examples, adding money to a saving account or withdrawing money from a saving account, gains and losses when playing a football game are situations that require both positive and negative numbers.
In football, for instance, a gain of 10 yards on the first play can be written as +10 yards or just 10.
However, a lost of 6 yards on the second play can be written as -6.
All positive numbers, negative numbers, and zero can be put on number line. The following is a number line:
The arrows at both ends show that the numbers do not stop after 7 or -7 but the pattern continues.
You may have noticed that all numbers on the right of zero are positive. On the other hand, all numbers on the left of 0 zero are negative.
We need directions as well as an amount when working with numbers.
Going to the right usually means that you are going in the positive direction whereas going to the left means that you are going in the negative direction
With the exception of zero, for every number on the number line, there exist an opposite number on the other side.
Opposites numbers are located at the same distance from zero.
For instance, 2 and -2 are opposites numbers because they are both 2 units away from zero.
By the same fashion, 698745 and -698745 are opposites
When you add two opposites numbers, the sum is always zero
for instance,
-3 + 3 = 3 + - 3 = 0
-698745 + 698745 = 0
The distance a number is from zero is called its absolute value.
The absolute value is often misunderstood by many. Always think of it as a distance.
For instance, the absolute value of 2 is 2 because the distance from 0 to 2 is 2.
The absolute value of -5 is 5 because the distance from 0 to -5 is 5.
In practice, we use the following notation: |2| and |-5|.
|2| is read "The absolute value of 2"
|-5| is read " The absolute value of -5 "
So, |2|= 2 and |-5|= 5
Notice that the absolute value of a number is always positive.