 Problem: George fan his friend Jeanne \$3. If he borrows an additional \$6, just how much will he owe her altogether?

Solution: This difficulty is fairly simple: just add \$3 and also \$6 and also the result is \$9.

You are watching: The sum of two negative integers is

The problem over can be solved using enhancement of integers. Owing \$3 have the right to be represented by -3 and also owing \$6 can be represented by -6. The trouble becomes:-3 + -6 = -9

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

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

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

 Adding negative Integers Integers Sum -2 + -9 = -11 -5 + -8 = -13 -13 + -7 = -20

Do no confuse the authorize of the integer with the operation being performed. Psychic that:-2 + -9 = -11 is review as Negative 2 plus an unfavorable 9 equals an adverse 11.

Rule: The amount of two positive integers is a positive integer.

Example 2: Find the amount of every pair that integers. Friend may attract a number heat to help you settle this problem.

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

Do not confuse the sign of the integer v the operation being performed. Mental that:

+29 + +16 = +45 is read as Positive 29 plus hopeful 16 equates to positive 45.

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

Procedure: To add a positive and a negative integer (or a an adverse and a optimistic integer), follow this steps:

1. Find the absolute value of every integer.

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

3. The result from step 2 bring away the authorize of the integer with the better absolute value.

We will usage the above procedure to add integers v unlike indications in instances 3 through 7. Describe the number heat to assist you visualize the procedure in each example. We will use money as 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 confident sign since +7 is farther indigenous zero than -4.

Solution 1: +7 + -4 = +3

Solution 2: If you start with \$7 and you fan \$4, then you end up through \$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 an adverse sign since -9 is farther indigenous 0 than +5.

Solution 1: -9 + +5 = -4

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

Example 5: Find the amount of +6 and -7.

Step 1: |+6| = 6 and |-7| = 7

Step 2: 7 - 6 = 1

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

Solution 1: +6 + -7 = -1

Solution 2: If you begin with \$6 and also you fan \$7, then you room still brief \$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 through \$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 essence 0 has actually no sign.

Solution 1: +9 + -9 = 0

Solution 2: If you start with \$9 and also you owe \$9, climate you end up through \$0.

In example 7 you will notice that the integers +9 and -9 are opposites. Look in ~ the difficulties below. Do you view a pattern?

-100 + +100 = 0

+349 + -349 = 0

-798 + +798 = 0

Rule: The amount of any integer and also its opposite is equal to zero.

Summary: Adding two confident integers always yields a hopeful sum; including two an unfavorable integers always yields a an adverse sum. To discover the sum of a positive and a an unfavorable integer, take the absolute value of every integer and also then subtract these values. The result takes the authorize of the integer v the larger absolute value. The sum of any type of integer and its the contrary is same to zero.

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### Exercises

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