Adding And Subtracting Integers Word Problems Worksheet With Answers Pdf

Adding and Subtracting Integers Word Problems Worksheet with Answers PDF: A Comprehensive Guide

Adding and subtracting integers can be tricky, but mastering these skills is crucial for success in higher-level math. Word problems, in particular, require a strong understanding of both the mathematical concepts and the ability to translate real-world scenarios into numerical equations. This article provides a comprehensive guide to solving integer word problems, complete with examples, strategies, and a simulated worksheet with answers. We'll cover various scenarios and offer tips to help you confidently tackle these types of problems.

Understanding Integers

Before diving into word problems, let's refresh our understanding of integers. Integers are whole numbers, including zero, and their negative counterparts. They extend infinitely in both positive and negative directions on the number line.

Key Concepts:

• Positive Integers: Numbers greater than zero (e.g., 1, 2, 3, ...).
• Negative Integers: Numbers less than zero (e.g., -1, -2, -3, ...).
• Zero: Neither positive nor negative.

Understanding the number line is crucial. Visualizing integers on a number line helps to understand their relative positions and the implications of addition and subtraction.

Strategies for Solving Integer Word Problems

Tackling integer word problems requires a systematic approach. Here's a step-by-step strategy:

1. Read Carefully: Thoroughly read the problem to understand the situation and what is being asked. Identify the key information and the unknown quantity you need to find.

2. Define Variables: Assign variables (like x, y, etc.) to represent the unknown quantities. Clearly label what each variable represents.

3. Translate into an Equation: Translate the word problem into a mathematical equation using the appropriate operations (addition or subtraction). Pay close attention to keywords that indicate addition (e.g., "increased by," "more than," "total") or subtraction (e.g., "decreased by," "less than," "difference").

4. Solve the Equation: Use the rules of integer addition and subtraction to solve the equation. Remember the rules for adding and subtracting integers:

   • Adding Integers:

     • Same signs: Add the absolute values and keep the common sign. (e.g., -3 + (-5) = -8)
     • Different signs: Subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. (e.g., -7 + 4 = -3)

   • Subtracting Integers: Change the subtraction problem to an addition problem by adding the opposite of the second number. (e.g., 5 - (-2) = 5 + 2 = 7)

5. Check Your Answer: After solving, check your answer to ensure it makes sense in the context of the word problem. Does the answer logically fit the situation described?

Example Word Problems and Solutions

Let's work through some example problems to illustrate these strategies:

Problem 1: The temperature at noon was 5°C. By evening, the temperature dropped by 8°C. What was the temperature in the evening?

Solution:

1. Read: The problem involves a temperature change.
2. Define: Let x represent the evening temperature.
3. Equation: 5°C - 8°C = x
4. Solve: x = -3°C
5. Check: A drop of 8°C from 5°C results in a temperature of -3°C.

Problem 2: A submarine is at a depth of -250 meters. It ascends 150 meters. What is its new depth?

Solution:

1. Read: The problem describes the submarine's vertical movement.
2. Define: Let x represent the new depth.
3. Equation: -250 meters + 150 meters = x
4. Solve: x = -100 meters
5. Check: Ascending 150 meters from -250 meters leaves the submarine at -100 meters.

Problem 3: John has $20 in his bank account. He deposits $35 and then withdraws $50. What is his final balance?

Solution:

1. Read: The problem involves financial transactions.
2. Define: Let x represent the final balance.
3. Equation: $20 + $35 - $50 = x
4. Solve: x = $5
5. Check: Adding $35 to $20 and then subtracting $50 results in a balance of $5.

Problem 4: A mountain climber ascends 200 meters, then descends 75 meters, and finally ascends another 125 meters. What is the climber's net change in altitude?

Solution:

1. Read: The problem tracks changes in altitude.
2. Define: Let x represent the net change in altitude.
3. Equation: 200 meters + (-75 meters) + 125 meters = x
4. Solve: x = 250 meters
5. Check: Adding the ascents and subtracting the descent gives a net change of 250 meters.

Simulated Worksheet with Answers

Below is a simulated worksheet with various integer word problems. Try solving them using the strategies discussed above. The answers are provided below the worksheet.

(Simulated Worksheet)

1. A diver descends 15 meters, then ascends 8 meters. What is the diver's final depth?
2. The temperature was -5°C. It increased by 12°C. What is the new temperature?
3. A company made a profit of $5000 in January and a loss of $2000 in February. What was the company's net profit or loss for the two months?
4. An elevator starts on the 10th floor, goes down 7 floors, and then up 5 floors. What floor is the elevator on?
5. A football team gained 15 yards, then lost 8 yards, and finally gained 12 yards. What was their total yardage gain?
6. Sarah owed her friend $25. She paid back $10. How much does she still owe?
7. The stock market went up 30 points, then down 15 points, and then up 20 points. What was the net change in points?
8. A submarine was at a depth of -300 meters. It ascended 180 meters. Then it descended 50 meters. What is its final depth?
9. The highest point in a city is 1200 feet above sea level, and the lowest point is 200 feet below sea level. What is the difference in elevation between the highest and lowest points?
10. A plane is flying at an altitude of 30,000 feet. It descends 5,000 feet and then ascends 2,000 feet. What is its new altitude?

(Answers to the Simulated Worksheet)

1. -7 meters
2. 7°C
3. $3000 profit
4. 8th floor
5. 19 yards
6. $15
7. 35 points
8. -170 meters
9. 1400 feet
10. 27,000 feet

Further Practice and Resources

Regular practice is key to mastering integer word problems. You can find additional practice problems in textbooks, online resources, and educational websites. Remember to focus on understanding the concepts and developing a systematic approach to problem-solving. By consistently applying the strategies outlined in this article, you can build your confidence and improve your ability to solve integer word problems effectively. Remember to visualize the problems using a number line and break down complex problems into smaller, manageable steps. Good luck!