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. 

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