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Here are four great examples about adding integers word problems. Read the solution carefully, so you will know how to do similar problems.

Problem #1:

Maria saved 200 dollars and then she spent 150 dollars. How much money does Maria have now? Solution The problem has 3 important components shown in bold below. Maria saved 200 dollars and then she spent 150 dollars. How much money does Maria have now? Saved 200 can be represented by + 200 And is the + sign Spent 150 can be represented by -150 We get 200 + -150 and 200 + -150 = 50 Maria has 50 dollars left.

Problem #2:

A submarine at 21 feet below sea level suddenly moves up about 6 feet. At what depth is the submarine located now? Solution The problem has 2 important components shown in bold below. A submarine at 21 feet below sea level suddenly moves up about 6 feet . At what depth is the submarine located now? 21 feet below sea level can be represented by - 21 We can use the + sign Moves up about 6 feet can be represented by +6 We get -21 + +6 and -21 + +6 = -15 The submarine is 15 feet below sea level.

Problem #3:

A football team gained 6 yards and then lost 10 yards. Where is the football team now? Solution The problem has 3 important components shown in bold below. A football team gained 6 yards and then lost 10 yards. Where is the football team now? Gained 6 can be represented by + 6 And is the + sign Lost 10 can be represented by -10 We get +6 + -10 and +6 + -10 = -4 Overall the football team has lost 4 yards.

Problem #4:

Steve had 140 dollars. He loaned 50 dollars to a friend, spent 31 dollars, and received his 80 dollars paycheck from work. How much money does he have now? Solution The problem has 4 important components shown in bold below. Steve had 140 dollars . He loaned 50 dollars to a friend , spent 31 dollars, and received his 80 dollars paycheck from work. How much money does he have now? Had 140 dollars can be represented with +140 Loaned 50 can be represented by -50 Spent 31 can be represented by -31 Received his 80 can be represented by +80 We get +140 + -50 + -31 + +80 +140 + -50 + -31 + +80 = (140 + -50) + -31 + +80 = 90 + -31 + +80 = (90 + -31) + +80 = 59 + +80 = 139

Steve has now 139 dollars.

Subtracting integers word problems

adding integers

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Integer addition, learn about integer addition with example problems and interactive exercises..

Solution: This problem is quite simple: just add $3 and $6 and the result is $9.

The problem above can be solved using addition of integers . Owing $3 can be represented by - 3 and owing $6 can be represented by - 6. The problem becomes: - 3 + - 6 = - 9

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

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

Example 1: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.

Do not confuse the sign of the integer with the operation being performed. Remember that: - 2 + - 9 = - 11 is read as Negative 2 plus negative 9 equals negative 11.

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

Example 2: Find the sum of each pair of integers. You may draw a number line to help you solve this problem.

Do not confuse the sign of the integer with the operation being performed. Remember that:

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

So far we have added integers with like signs (either both negative or both positive). What happens when we add integers with unlike signs? How do we 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:

1. Find the absolute value of each integer.

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

3. The result from Step 2 takes the sign of the integer with the greater absolute value.

We will use the above procedure to add integers with unlike signs in Examples 3 through 7. Refer to the number line to help you visualize the process in each example. We will use money as an alternative method for adding integers.

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

Step 1: | + 7| = 7 and | - 4| = 4

Step 2: 7 - 4 = 3

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

Solution 1: + 7 + - 4 = + 3

Solution 2: If you start with $7 and you owe $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 negative sign since - 9 is farther from 0 than + 5.

Solution 1: - 9 + + 5 = - 4

Solution 2: If you owe $9 and you are paid $5, then you are still short $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 negative 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, then you are still short $1.

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

Step 1: | - 6| = 6 and | + 7| = 7

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 you are paid $7, then you end up with $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 integer 0 has no sign.

Solution 1: + 9 + - 9 = 0

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

In Example 7 you will notice that the integers + 9 and - 9 are opposites . Look at the problems below. Do you see a pattern?

- 100 + + 100 = 0

+ 349 + - 349 = 0

- 798 + + 798 = 0

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

Summary: Adding two positive integers always yields a positive sum; adding 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 any integer and its opposite is equal to zero.

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

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adding integers word problems

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Adding Integers and Subtracting Integers

In these lessons, we will look at adding integers and subtracting integers using the number line and using rules.

Using the Number Line

When we add , we move right on the number line.

When we subtract , we move left on the number line

Adding Integers

To evaluate –3 + 2 , we start at –3 and move 2 places to the right

The answer is –1

Subtracting integers

To evaluate –3 – 2 , we start at –3 and move 2 places to the left

The answer is –5

How to add integers and subtract integers using the number line?

How to think about adding and subtracting integers on a number line?

Using Rules to Add Integers

Using the number line to add or subtract integers may be quite tedious. A quicker method would be to use the following rules:

The sum of two or more positive integers is a positive integer. The sum of two or more negative integers is a negative integer.

(+7) + (+ 4) = + 11 (– 8) + (– 9) = – 17

To find the sum of a positive and a negative integer: Subtract the two numbers (ignore the signs) and then keep the sign of the larger integer.

(– 9) + (+ 7) = – 2 (– 3) + (+ 5) = + 2

The sum of an integer and its opposite is equal to zero

(– 9) + (+ 9) = 0 (– 3) + (+ 3) = 0

How to use the rules to add integers?

Using Rules to Subtract Integers

To subtract integers, we can rewrite the subtraction problem as an addition problem. Instead of subtracting, we add the opposite.

Subtracting a positive is the same as adding a negative. 3 − (4) = 3 + (−4)

Subtracting a negative is the same as adding a positive. 3 − (− 4) = 3 + 4

We then follow the rules for adding integers.

Basic rules for subtracting integers and provides examples Each subtraction problem is rewritten as an addition problem.

Subtracting Integers using Rules

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Application of integer operations

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COMMENTS

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How to Solve Word Problems with Addition or Subtraction of Integers ; Step 1: Write out an equation that represents the word problem ; Step 2: Solve the equation