Adding & Subtracting Integers: Word Problems Worksheet Answers
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Adding and subtracting integers can sometimes seem daunting, especially when faced with word problems. However, breaking down the process step-by-step can greatly enhance understanding and confidence in tackling these problems. In this article, we will explore various techniques and tips for solving integer word problems and provide solutions to common worksheets that focus on adding and subtracting integers.
Understanding Integers
What are Integers?
Integers are whole numbers that can be positive, negative, or zero. Examples of integers include -3, 0, and 5. When dealing with word problems, understanding the context is key to identifying whether you are adding or subtracting integers.
Key Concepts in Adding and Subtracting Integers
Addition of Integers
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Same Signs: When adding two integers with the same sign, add their absolute values and keep the common sign.
- Example: ( 3 + 5 = 8 ) and ( -3 + (-5) = -8 )
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Different Signs: When adding two integers with different signs, subtract their absolute values and keep the sign of the integer with the larger absolute value.
- Example: ( 5 + (-3) = 2 ) and ( -5 + 3 = -2 )
Subtraction of Integers
Subtraction can be transformed into addition by changing the sign of the number being subtracted:
[ a - b = a + (-b) ]
Word Problems
Word problems may be straightforward or complex, but identifying keywords can help determine whether to add or subtract. Here are some common keywords:
- Addition Keywords: total, sum, in all, together, increased by.
- Subtraction Keywords: difference, less than, remaining, decreased by, how many more.
Example Word Problems and Solutions
Below are sample word problems along with their solutions to help illustrate how to approach adding and subtracting integers.
Problem 1: The Temperature Change
Problem Statement: The temperature in the morning was 12°C. By afternoon, the temperature dropped by 7°C. What is the afternoon temperature?
Solution:
This problem requires subtraction.
- Initial temperature: ( 12 , °C )
- Temperature drop: ( 7 , °C )
Using the subtraction method: [ 12 - 7 = 5 ]
Final Answer: The afternoon temperature is 5°C.
Problem 2: Elevation Levels
Problem Statement: A submarine is at a depth of 150 meters below sea level. It rises 70 meters. What is the new depth of the submarine?
Solution:
This problem requires addition since we are adding a positive elevation change to a negative depth.
- Initial depth: ( -150 , m )
- Elevation change: ( 70 , m )
Using the addition method: [ -150 + 70 = -80 ]
Final Answer: The new depth of the submarine is 80 meters below sea level.
Problem 3: Banking Transactions
Problem Statement: You have $200 in your bank account. You withdraw $45 and then deposit $80. How much is in your account now?
Solution:
First, we need to subtract the withdrawal and then add the deposit.
- Initial amount: ( 200 )
- Withdrawal: ( -45 )
- Deposit: ( 80 )
First, perform the subtraction: [ 200 - 45 = 155 ]
Then, add the deposit: [ 155 + 80 = 235 ]
Final Answer: You now have $235 in your bank account.
Table of Common Operations with Integers
Here’s a quick reference table for adding and subtracting integers:
<table> <tr> <th>Operation</th> <th>Example</th> <th>Result</th> </tr> <tr> <td>Add same signs</td> <td>3 + 5</td> <td>8</td> </tr> <tr> <td>Add different signs</td> <td>5 + (-3)</td> <td>2</td> </tr> <tr> <td>Subtract</td> <td>12 - 7</td> <td>5</td> </tr> <tr> <td>Combine operations</td> <td>200 - 45 + 80</td> <td>235</td> </tr> </table>
Tips for Solving Integer Word Problems
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Read Carefully: Pay attention to what the problem is asking. Look for keywords that indicate whether to add or subtract.
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Write it Down: Write out the mathematical expression that represents the word problem before solving it. This helps clarify your thoughts.
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Use a Number Line: Visualizing the problem on a number line can help in understanding the operations involved.
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Check Your Work: After calculating, always go back and check if the answer makes sense in the context of the problem.
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Practice Makes Perfect: The more you practice word problems, the more intuitive they will become.
Important Note:
“Understanding the context of a problem is crucial for determining whether to add or subtract. Always refer back to the original question to ensure you’ve answered correctly.”
By mastering the concepts of adding and subtracting integers and applying them to real-world scenarios, you can enhance your problem-solving skills and gain confidence in math. Whether it's a simple temperature change or managing your finances, these skills are invaluable. Keep practicing, and you'll become an expert in no time!