7th Grade Algebra: Adding and Subtracting Integers

How to Add and Subtract Integers for 7th Grade Algebra

What Are Integers?

Integers are whole numbers, both negative and positive, on a number line. For example, 1, -1 and 0 are all integers. Fractions and decimals such as 1/2, -3/4, 0.05 and -0.6 are not integers.

Using a Number Line

Learning to add and subtract integers can be easier if you use a number line. On a number line, positive numbers are to the right of zero, and negative numbers are to the left. With both positive and negative numbers, move to the right when adding and to the left when subtracting. Consider the following examples.

• Positive + Positive
  Add 3 + 5. Begin at 0 on the number line, move three digits to the right (arriving at 3), and then move five digits to the right (to add 5). This brings you to 8 on the number line, which is the answer to 3 + 5.
  
  
• Negative + Negative
  Add (-3) + (-5). Begin at 0 and move three digits to the left (-3) and then move five digits to the left (to subtract -5). The answer is -8.
  
  
• Positive + Negative
  Add 3 + (-5). Begin at 0 and move three digits to the right (3), and then move five digits to the left for the (-5). You should land on (-2), which is the answer to 3 + (-5).
  
  

Rules for Adding and Subtracting Integers

• Positive + Positive = Positive
  A positive integer plus another positive integer will always produce a positive answer. For instance, 5 + 6 = 11
  
  
• Negative + Negative = Negative
  Adding two negative numbers will always give you a negative answer. Think of it terms of bad deeds. Two negative situations will only make things worse. In an equation, you would write it like this: (-5) + (-6) = -11
  
  
• Minus = Plus Negative
  Never subtract integers. Instead, turn the minus sign into a plus negative and add the integers. For instance, if your problem is (-5) - 6, convert it to (-5) + (-6). Your answer will be -11.
  
  
• Minus a Minus Negative = Plus
  When you find a minus sign and a negative sign directly adjacent to each other, convert them into one plus sign. For example, in 5 - (-6), convert the -(-) symbols so the problem reads: 5 + 6 = 11.
  
  
• Positive + Negative = Positive or Negative
  When you add a positive and negative number together, the answer will always be the difference between the absolute value of each number. However, you will determine the negative or positive value of your answer by making it the same value as the largest absolute value. For instance, 5 + (-6) = -1 because the difference between |5| and |6| is 1, and |6| is larger than |5|, so the answer is negative. If the problem was (-5) + 6, your answer would be a positive 1.