Integers 

Basically, integers are used to represent situations that whole numbers are not able to represent mathematically. For examples the following are situations that require both positive and negative numbers. Start with the interactive lesson below.

• Adding money to a saving account or withdrawing money from a saving account.
• Gains and losses when playing a football game.
• Rise or fall in temperature

Learn more about integers

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. By the same token, if you withdraw 50 dollars from the bank, this can be represented with -50. If you deposit 50 dollars instead then we write 50.

The following is a number line showing integers from -10 to 10. However, the arrows at both ends show that the numbers do not stop after 10 or -10 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.

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 opposite numbers, the sum is always zero.

For examples, -3 + 3 = 3 + - 3 = 0 and -698745 + 698745 = 0

Absolute Value of an Integer

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