Create and Solve a Word Problem That Adds Positive Integers and Negative Integers Easy

Larn About Integer Improver With Example Problems And Interactive Exercises.

Problem: George owes his friend Jeanne $3. If he borrows another $6, how much volition he owe her altogether?

Solution: This problem is quite simple: just add $3 and $six and the result is $9.

The problem higher up tin can be solved using add-on of integers. Owing $three tin be represented by^-three and owing $6 tin be represented past^-6. The problem becomes:
^-3 +^-6 =^-9

Look at the number line below. If we kickoff at 0, and move three to the left, we land on^-3. If nosotros then move another 6 to the left, we terminate up at^-9.

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Rule: The sum of ii negative integers is a negative integer.

Example ane: Observe the sum of each pair of integers. Yous may draw a number line to assist you solve this problem.

Adding Negative Integers
Integers	Sum
-2 +-9 =	-11
-5 +-eight =	-xiii
-13 +-vii =	-xx

Do not confuse the sign of the integer with the functioning beingness performed. Think that:^-2 +^-9 =^-11 is read asNegative 2 plus negative 9 equals negative 11.

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Dominion: The sum of 2 positive integers is a positive integer.

Example ii: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.

Adding Positive Integers
Integers	Sum
+2 ++9 =	+11
+17 ++5 =	+22
+29 ++xvi =	+45

Exercise not confuse the sign of the integer with the operation existence performed. Recall that:

⁺29 +⁺16 =⁺45 is read asPositive 29 plus positive xvi equals positive 45.

So far nosotros accept added integers with similar signs (either both negative or both positive). What happens when nosotros add integers with unlike signs? How exercise nosotros add a positive and a negative integer, or a negative and a positive integer?

Procedure: To add a positive and a negative integer (or a negative and a positive integer), follow these steps:

ane. Discover the absolute value of each integer.

2. Subtract the smaller number from the larger number you get in Pace 1.

iii. The issue from Step 2 takes the sign of the integer with the greater accented value.

We will use the above process to add together integers with dissimilar signs in Examples 3 through 7. Refer to the number line to aid you visualize the process in each case. Nosotros volition use coin equally an alternative method for calculation integers.

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Example 3: Detect the sum of⁺7 and^-4.

Pace 1: |⁺7| = 7 and |^-iv| = 4

Step 2: vii - 4 = 3

Stride 3: The number three volition take a positive sign since⁺7 is farther from nix than^-iv.

Solution 1:⁺7 +^-four =⁺three

Solution two: If you offset with $seven and you owe $4, and so you lot terminate up with $3.

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Example 4: Find the sum of^-nine and⁺5.

Pace one: |^-nine| = nine and |⁺5| = v

Stride 2: ix - 5 = 4

Pace three: The number 4 will take a negative sign since^-ix is farther from 0 than⁺v.

Solution 1:^-9 +⁺5 =^-4

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

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Instance five: Find the sum of⁺six and^-7.

Footstep 1: |⁺6| = 6 and |^-7| = 7

Pace ii: 7 - 6 = i

Step 3: The number 1 volition have a negative sign since^-7 is further from 0 than⁺6.

Solution one:⁺6 +^-vii =^-ane

Solution 2: If you lot start with $6 and yous owe $seven, so yous are still short $1.

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Example 6: Find the sum of^-six and⁺7.

Step 1: |^-6| = vi and |⁺7| = vii

Footstep two: 7 - 6 = 1

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

Solution 1:^-6 +⁺7 =⁺ane

Solution 2: If you lot owe $six and you are paid $seven, then you end upwards with $1.

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Case seven: Find the sum of⁺9 and^-ix.

Pace i: |⁺9| = 9 and |^-9| = nine

Step 2: 9 - 9 = 0

Step 3: The integer 0 has no sign.

Solution one:⁺nine +^-9 = 0

Solution 2: If you start with $nine and you lot owe $nine, so you end up with $0.

In Case vii you will notice that the integers⁺9 and^-ix are opposites. Look at the problems below. Do you encounter a pattern?

^-100 +⁺100 = 0

⁺349 +^-349 = 0

^-798 +⁺798 = 0

Rule:   The sum of whatever integer and its reverse is equal to zero.

Summary: Adding two positive integers always yields a positive sum; calculation two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The result takes the sign of the integer with the larger absolute value. The sum of whatever integer and its opposite is equal to cipher.

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Exercises

Directions: Read each question below. Click once in an ANSWER BOX and blazon in your respond; then click ENTER. After you click ENTER, a message volition appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

i.	-half dozen +-9 = ?

ii.	+7 ++11 = ?

3.	+5 +-3 = ?

4.	-2 ++seven = ?

5.	+9 +-12 = ?

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Source: https://www.mathgoodies.com/lessons/vol5/addition

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