Algebra Problems With Integers

Adding Integers

• Integers are made up of positive and negative numbers. The only number that is neutral is zero. Negative numbers always have their signs in front of them. Positive numbers may or may not have their signs in front of them. An example of this would be the number 1. It is understood to have a positive sign.

  Numbers that have the same sign in front of them can simply be added together. It does not matter if the sign is positive or negative.

  Some examples:

  8 + 3 = 11 (or +8 + 3)

  -14 -- 10 = -24 (or -14 + -10)

Subtracting Integers

• When adding integers, it is important to remember if the signs are the same, they are added together. If the signs are opposite, the numbers are subtracted and the sign of the bigger number is used.

  Some examples:

  7 -- 4 = 3

  -- 7 + 4 = - 3

  In the first example, 7 is positive, even though the sign is not shown. Since they are opposite signs, they are subtracted from each other and the positive sign of the 7 is used for the answer. In the second example, both signs are also opposite. The smaller number is always subtracted from the larger number. The positive 4 is subtracted from negative 7. The answer will use the sign from the larger number so the answer is -- 3.

Brackets or Parenthesis with Integers

• Brackets or parenthesis often create a lot of confusion for algebra students and can make algebra problems with Integers seem more complex than they really are. The most important thing to remember is to solve whatever is in the brackets before applying the rules of the positive and negative signs.

  If the number inside the bracket is negative, it must be changed into a positive sign. An example is below:

  - (4) = - 4

  -(-4) = +4 or 4

  A positive sign does not have to change when the bracket is opened.

  + (3) = 3

  Once the student remembers to change the numbers inside the brackets according to the sign, he will solve the problem according to the rules of positive and negative signs.

  Examples:

  --(5) -- (8)

  The brackets have negative signs in the front of them but the numbers are positive. So the brackets are opened and the numbers are changed to negative numbers.

  -5 -- 8 = -13

Multiplying and Dividing Integers

• A multiplication table is useful for multiplying integers. The sign of the answer is determined by whether the numbers have the same sign. If the signs are the same, the answer is positive. It does not matter if the signs are positive or negative. If the numbers have opposite signs, the answer is always negative.

  -4 x -3 = 12

  -4 (3) = -12

  Students will find the same rules apply for dividing integers as they do for multiplying integers.

  (-15)/ (-5) = 3

  (15)/ (-5) = -3