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Problem: George owes his friend Jeanne $3. If that borrows an additional $6, just how much will he owe she altogether?

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

You are watching: The sum of two negative integers is always

The problem above can be resolved using enhancement of integers. Fan $3 have the right to be represented by -3 and also owing $6 can be stood for by -6. The difficulty becomes:-3 + -6 = -9

Look at the number line below. If we start at 0, and also move 3 to the left, us land on -3. If us then move an additional 6 to the left, we end up at -9.

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

Example 1: Find the sum of every pair that integers. Friend may attract a number heat to aid you solve this problem.

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

 

Do no confuse the sign of the integer v the operation being performed. Psychic that:-2 + -9 = -11 is read as Negative 2 plus negative 9 equals negative 11.

Rule: The sum of two optimistic integers is a positive integer.

Example 2: Find the amount of every pair that integers. You may draw a number heat to assist you solve this problem.

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

Do no confuse the authorize of the integer through the procedure being performed. Psychic that:

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

So much we have added integers through like signs (either both an adverse or both positive). What happens as soon as we add integers with unlike signs? just how do we include a positive and a an unfavorable integer, or a an adverse and a hopeful integer?

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

1. Find the absolute value of each integer.

2. Subtract the smaller sized number indigenous the bigger number you acquire in action 1.

3. The an outcome from step 2 take away the authorize of the integer v the higher absolute value.

We will use the above procedure to add integers through unlike indicators in instances 3 v 7. Describe the number heat to assist you visualize the process in every example. Us will usage money together an alternative technique for adding 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 take a confident sign since +7 is farther native zero than -4.

Solution 1: +7 + -4 = +3

Solution 2: If you start with $7 and also you fan $4, climate you end up v $3.

Example 4: Find the amount of -9 and +5.

Step 1: |-9| = 9 and |+5| = 5

Step 2: 9 - 5 = 4

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

Solution 1: -9 + +5 = -4

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

Example 5: 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 take a negative sign since -7 is farther indigenous 0 than +6.

Solution 1: +6 + -7 = -1

Solution 2: If you start with $6 and you fan $7, then you space still brief $1.

Example 6: Find the sum of -6 and +7.

Step 1: |-6| = 6 and also |+7| = 7

Step 2: 7 - 6 = 1

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

Solution 1: -6 + +7 = +1

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

Example 7: Find the amount of +9 and -9.

Step 1: |+9| = 9 and |-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 fan $9, climate you end up with $0.

In instance 7 you will notice that the integers +9 and -9 are opposites. Look at the troubles below. Carry out you watch a pattern?

-100 + +100 = 0

+349 + -349 = 0

-798 + +798 = 0

Rule: The sum of any type of integer and its opposite is equal to zero.

Summary: Adding two hopeful integers constantly yields a positive sum; adding two negative integers always yields a an adverse sum. To discover the sum of a positive and a negative integer, take it the absolute worth of each integer and then subtract these values. The result takes the authorize of the integer v the bigger absolute value. The sum of any type of integer and its opposite is same to zero.

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Exercises

Directions: review each concern below. Click as soon as in an answer BOX and kind in her answer; climate click ENTER. After girlfriend click ENTER, a post will appear in the outcomes BOX to suggest whether her answer is correct or incorrect. To begin over, click CLEAR.