Integers

Lets talk a little about integers.  An integer is

• the natural numbers {1, 2, 3, 4, 5, ...} or positive integers
• the negative integers {....-5, -4, -3, -2, -1}
• the number 0

Basically an integer is any whole number, positive, negative or zero. So, what happens when we use positive and negative integers with adding, subtracting, multiplying and dividing?  Lets discuss some basic rules.

Adding Integers

• Adding two positive integers will leave you with a positive answer.
•  7 + 6 = 13
• Adding two negative integers will leave you with a negative answer.
•  (-3) + (-9) =  -12
• When adding a positive integers to a negative integer, subtract the smaller number from the larger number and use the sign of the integer with the larger absolute value.
• 9 + (-5) = 9 - 5 = 4 (using the sign from the larger integer which is positive)
• (-9) + 5 = 9 - 5 = 4 = -4 (using the sign of the larger number which is negative)

 Subtracting Integers

• When subtracting two positive integers
• Take the smaller integer away from the larger integer and you will get a positive integer.
• 13 - 4 = 9 
• Take the larger integer away from the smaller integer and you will get a negative integer.  Subtract the larger integer from the smaller integer and add a negative sign.
• 5 - 10 = 10 - 5 = 5 = -5
• Subtracting two negative integers, change the minus and negative sign to a plus and follow the addition rules for adding a positive and negative number.
• (-7) - (-6) = (-7) + 6 = 7 - 6 = 1 = -1
• (-4) - (-8) = (-4) + 8 = 8 - 4 = 4
• Subtracting a positive integer and a negative integer, add the two integers together and use the sign from the integer with the largest absolute.
•  19 - (-4) = 19 + 4 = 23
• (-19) - 4 = 19 + 4 = 23 = -23

Here is a great video explaining how easy it is to add and subtract integers using the rules previously described. It also shows a few other methods for adding and subtracting integers.

Multiplying Integers

• Multiplying two positive integers leaves you with a positive answer.
• 4 x 6 = 24
• Multiplying two negative integers leaves you with a negative answer.
•  (-5) x (-3) = -15
• Multiplying a positive and a negative integer leaves you with a negative answer.
• (-4) x 7 = -28

Dividing Integers

• Dividing two positive integers leaves you with a positive answer
• 24/6 = 4
• Dividing two negative integers leaves you with a positive answer
•  (-9)/(-3) = 3
• Dividing a positive and a negative integer leaves you with a negative answer
• (-25)/5 = -5
• 21/(-3) = -7

Here is another great video explaining how to multiply and divide integers.

I hope this helped you learned a little bit about adding, subtracting, multiplying and dividing positive and negative integer.s