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

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

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The problem over can be resolved using addition of integers. Fan \$3 deserve to be stood for by -3 and owing \$6 deserve to be stood for by -6. The problem becomes:-3 + -6 = -9

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

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

Example 1: Find the amount of each pair of integers. Girlfriend may attract a number heat to help you solve this problem.

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

Do not confuse the authorize of the integer through the procedure being performed. Psychic that:-2 + -9 = -11 is review as Negative 2 plus negative 9 equals an unfavorable 11.

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

Example 2: Find the sum of every pair the integers. You may attract a number heat to aid you settle this problem.

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

Do no confuse the authorize of the integer with the operation being performed. Remember that:

+29 + +16 = +45 is review as Positive 29 plus confident 16 equates to positive 45.

So far we have included integers v like indicators (either both an adverse or both positive). What happens once we include integers v unlike signs? just how do we include a positive and a an adverse integer, or a negative and a confident integer?

Procedure: To include a positive and also a an unfavorable integer (or a an adverse and a confident integer), follow these steps:

1. Find the absolute value of every integer.

2. Subtract the smaller number from the bigger number you obtain in action 1.

3. The result from action 2 takes the authorize of the integer v the greater absolute value.

We will usage the above procedure to include integers with unlike indicators in examples 3 v 7. Describe the number line to aid you visualize the procedure in each example. We will usage money together an alternative technique for adding integers.

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

Step 1: |+7| = 7 and also |-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, then you end up with \$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 fan \$9 and also you space paid \$5, then you room still brief \$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 indigenous 0 than +6.

Solution 1: +6 + -7 = -1

Solution 2: If you start with \$6 and you fan \$7, then you are 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 take a hopeful sign since +7 is farther native 0 than -6.

Solution 1: -6 + +7 = +1

Solution 2: If you fan \$6 and also you are paid \$7, climate you end up v \$1.

Example 7: Find the sum of +9 and -9.

Step 1: |+9| = 9 and |-9| = 9

Step 2: 9 - 9 = 0

Step 3: The creature 0 has actually no sign.

Solution 1: +9 + -9 = 0

Solution 2: If you begin with \$9 and also you fan \$9, climate you finish up through \$0.

In instance 7 you will notification that the integers +9 and -9 are opposites. Look at the problems below. Do you view a pattern?

-100 + +100 = 0

+349 + -349 = 0

-798 + +798 = 0

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

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

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### Exercises

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