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.
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.
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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