Adding and Subtracting With Negative Integers

Now that the students have had an opportunity to refresh their memories about adding and subtracting integers on a number line, it is time for them to use the rules to find sums and differences of integers.

• Say: You've used a number line to add and subtract integers. When adding two positive integers, what will the sign of the sum be?(positive)
  What would be the sign of the sum if we added two negative integers?(negative)
  

• Ask: When adding a positive and a negative integer, how do you determine the sign of the sum?
  They should respond that the sum has the same sign as the number that is farthest from zero. That is, when adding ^–8 and ⁺5, the sum is negative since ^–8 is farther from zero than is ⁺5.

• Ask: How do you find the number part of the sum of a positive and negative integer?
  The number for the sum is the difference between the distances for the two numbers regardless of their direction. For example, ^–8 + 5 = ^–(8 – 5) or ^–3. Give the students several examples for them to do without using a number line: 23 + ^–15; ^–17 + 8; ^–35 + 47;16 + (^–34); ^–24 + (^–13).

• Say: Yesterday we mentioned that addition and subtraction are inverse operations. How did we do subtraction on the number line yesterday?
  Someone will say that you go to the first number and then move the number of units shown in the second number, but in the opposite direction of its sign. That is, to find 4 – (^–3), you go to ⁺4, then go three units in the opposite direction of the sign. Since the sign is negative — indicating a move to the left — move three units to the right instead. In this case subtracting ^–3 is like adding ⁺3. Have students do the following problem ^–4 – (⁺6).

• Say: Find an addition problem that is similar to each of the subtraction problems that follow and which gives the same answer: 3 – (^–4);6 – (2); ^–5 – (⁺2); ^–15 – (^–7).
  

• Ask: What is another way to do a subtraction problem involving integers?
  Discuss how you could change the sign of the number to be subtracted and follow the rules for adding integers.

  Have them find the answers to the following: 31 – (^–21);  ^–18 – (⁺23);  ^–21 – (^–17).