# APPLYING ADDITION AND SUBTRACTION OF INTEGERS

## Solving a Multistep Problem

You can use what you know about adding and subtracting integers to solve a multistep problem.

Example :

A seal is swimming in the ocean 5 feet below sea level. It dives down 12 feet to catch some fish. Then, the seal swims 8 feet up towards the surface with its catch. What is the seal’s final elevation relative to sea level ?

Solution : Step 1 :

The seal starts at 5 feet below the surface, so its initial position is -5 ft.

Write an expression.

Starts  - Dives down + Swims up

-5  -  12  +  8

Step 2 :

Add or subtract from left to right to find the value of the expression.

-5  -  12  +  8  =  -17  +  8

=  -9

The seal’s final elevation is 9 feet below sea level.

## Applying Properties to Solve Problems

You can use properties of addition to solve problems involving integers.

Example :

Jack has a checking account. On Monday he writes a \$160 check for groceries. Then he deposits \$125. Finally he writes another check for \$40. What was the total change in the amount in Jack’s account ?

Analyze Information :

When Jack deposits money, he adds that amount to the account. When he writes a check, that money is deducted from the account.

Formulate a Plan :

Use a positive integer for the amount Jack added to the account. Use negative integers for the checks he wrote. Find the sum.

-160 + 125 + (-40)

Solve :

Add the amounts to find the total change in the account. Use properties of addition to simplify calculations.

Commutative Property :

-160 + 125 + (-40)  =  -160 + (-40) + 125

Associative Property :

=  -200 + 125

=  -75

The amount in the account decreased by \$75.

Justify and Evaluate :

Jack's account has \$75 less than it did before Monday. This is reasonable because he wrote checks for \$200 but only deposited \$125.

## Practice Problems

Problem 1 :

Anna is in a cave 40 feet below the cave entrance. She descends 13 feet, then ascends 18 feet. Find her new position relative to the cave entrance.

Solution :

Step 1 :

Anna starts at 40 feet below cave entrance, so her initial position is -40 ft.

Write an expression.

Starts  - Descends + Ascends

-40  -  13  +  18

Step 2 :

Add or subtract from left to right to find the value of the expression.

-40  -  13  +  18  =  -53  +  18

=  -35

Anna's new position is 35 feet below the cave entrance.

Problem 2 :

Tomas works as an underwater photographer. He starts at a position that is 15 feet below sea level. He rises 9 feet, then descends 12 feet to take a photo of a coral reef. Write and evaluate an expression to find his position relative to sea level when he took the photo.

Solution :

Step 1 :

Tomas starts at 15 feet below sea level, so his initial position is -15 ft.

Write an expression.

Starts  + Rises - Descends

-15  +  9  -  12

Step 2 :

Add or subtract from left to right to find the value of the expression.

-15  +  9  -  12  =  -6  -  12

=  -18

When Tomas takes photo, his position is 18 feet below the sea level. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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