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Problem: George owes his girlfriend Jeanne $3. If the borrows another $6, how much will certainly he owe she altogether?

Solution: This difficulty is rather simple: just include $3 and $6 and the an outcome is $9.

You are watching: Is the sum of two integers positive negative or zero

The problem above can be fixed using enhancement of integers. Fan $3 can be represented by -3 and owing $6 deserve to be represented by -6. The problem becomes:-3 + -6 = -9

Look in ~ the number heat below. If we begin at 0, and move 3 come the left, we land on -3. If we then move an additional 6 come the left, we finish up at -9.

Rule: The amount of two negative integers is a an adverse integer.

Example 1: Find the amount of each pair that integers. You may attract a number line to assist you settle this problem.

Adding an adverse Integers
IntegersSum
-2 + -9 =-11
-5 + -8 =-13
-13 + -7 =-20

 

Do not confuse the sign of the integer with the procedure being performed. Mental that:-2 + -9 = -11 is check out as Negative 2 plus negative 9 equals an adverse 11.

Rule: The sum of two hopeful integers is a confident integer.

Example 2: Find the amount of each pair the integers. Girlfriend may attract a number heat to assist you deal with this problem.

Adding confident Integers
IntegersSum
+2 + +9 =+11
+17 + +5 =+22
+29 + +16 =+45

Do not confuse the sign of the integer through the procedure being performed. Mental that:

+29 + +16 = +45 is review as Positive 29 plus positive 16 equals positive 45.

So far we have added integers with like indicators (either both an unfavorable or both positive). What happens once we include integers with unlike signs? how do we add a positive and also a an adverse integer, or a an adverse and a optimistic integer?

Procedure: To add a positive and a an unfavorable integer (or a an unfavorable and a hopeful integer), follow these steps:

1. Find the absolute value of every integer.

2. Subtract the smaller sized number native the larger number you obtain in step 1.

3. The an outcome from step 2 bring away the authorize of the integer through the better absolute value.

We will usage the over procedure to include integers through unlike signs in examples 3 v 7. Describe the number line to help you visualize the process in each example. We will use money together an alternative an approach for including integers.

Example 3: Find the amount of +7 and -4.

Step 1: |+7| = 7 and |-4| = 4

Step 2: 7 - 4 = 3

Step 3: The number 3 will certainly take a positive sign since +7 is farther from zero than -4.

Solution 1: +7 + -4 = +3

Solution 2: If you begin with $7 and also you fan $4, then you finish up v $3.

Example 4: Find the sum of -9 and +5.

Step 1: |-9| = 9 and |+5| = 5

Step 2: 9 - 5 = 4

Step 3: The number 4 will take a negative sign since -9 is farther native 0 than +5.

Solution 1: -9 + +5 = -4

Solution 2: If you owe $9 and also you are paid $5, then you room still quick $4.

Example 5: Find the sum of +6 and -7.

Step 1: |+6| = 6 and |-7| = 7

Step 2: 7 - 6 = 1

Step 3: The number 1 will take a an unfavorable sign since -7 is farther from 0 than +6.

Solution 1: +6 + -7 = -1

Solution 2: If you start with $6 and you owe $7, climate you space still short $1.

Example 6: Find the amount of -6 and +7.

Step 1: |-6| = 6 and also |+7| = 7

Step 2: 7 - 6 = 1

Step 3: The number 1 will certainly take a optimistic sign since +7 is farther native 0 than -6.

Solution 1: -6 + +7 = +1

Solution 2: If you owe $6 and also you are paid $7, then you finish up v $1.

Example 7: Find the sum of +9 and -9.

Step 1: |+9| = 9 and also |-9| = 9

Step 2: 9 - 9 = 0

Step 3: The integer 0 has no sign.

Solution 1: +9 + -9 = 0

Solution 2: If you begin with $9 and also you owe $9, then you end up v $0.

In example 7 friend will an alert that the integers +9 and -9 are opposites. Look in ~ the troubles below. Carry out you view a pattern?

-100 + +100 = 0

+349 + -349 = 0

-798 + +798 = 0

Rule: The amount of any type of integer and also its the contrary is equal to zero.

Summary: Adding two hopeful integers constantly yields a confident sum; adding two an unfavorable integers constantly yields a an unfavorable sum. To uncover the sum of a positive and a an adverse integer, take it the absolute value of each integer and also then subtract this values. The result takes the authorize of the integer through the larger absolute value. The sum of any type of integer and also its opposite is same to zero.

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Exercises

Directions: read each inquiry below. Click once in solution BOX and form in her answer; climate click ENTER. After girlfriend click ENTER, a article will show up in the outcomes BOX to indicate whether your answer is exactly or incorrect. To begin over, click CLEAR.