Operations with Integers

Adding, Subtracting, Multiplying, and Dividing Integers

What are integers?

Integers are whole numbers that can be positive or negative and zero.

These RULES are important to do the operations with integers:

  • - x - = +
  • + x + = +
  • - x + = -
  • + x - = -

Adding Integers

If the integers have the same sign, add them together and keep the sign. If the integers have different signs subtract them. The answer takes the sign of the biggest number.


For example: 3 -(-11)


The answer will be 14 because you first take out the parentheses by multiplying the negative signs (they will turn to a positive). So, 3 + 11 will be 14.


Steps:

1. 9-(-5)

2. - x - = +

3. 9+5= 14


+9+3= 12

Subtracting Integers

What you need to do for subtracting is change the sign on the integer that is going to be subtracted. So, if in your equation you have a + and - you subtract and if you have a - and + subtract too. At the end subtract.


11+(-7)

The answer will be 4 because + and - make a -, so 11-7= 4


-2-(-6) = -2+6 Why? Because the two negative signs that are close together make a positive. So it will be -2+6. This equals 4 because, you do 6-2 and you take the sign of the biggest number that is 6, and since it´s positive, the answer will be positive too.


Another easy example: 13-5= 8

Multiplying and Dividing Integers

To multiply and divide integers you always multiply or divide. The product of two positive integers or two negative integers is positive. The product of a positive integer and a negative integer is negative.


For example:

-6 x 3= -18

Negative 18 because -6 is negative and the 3 is positive, and negative and positive make a negative. So the answer will be negative: -18.


-9 / -3= 3

The answer is positive 3 because, -9 is negative and -3 is negative too. So two negatives make the answer positive: 3. And then you divide normally.


Example: -5 x -4= 20