Adding And Subtracting Integers Word Problems Worksheet

Adding and Subtracting Integers: Word Problems Worksheet – A Comprehensive Guide

Mastering integer arithmetic is a crucial stepping stone in your mathematical journey. Understanding how to add and subtract integers is essential not only for academic success but also for navigating everyday life scenarios involving money, temperature, and more. This comprehensive guide will equip you with the skills and strategies needed to tackle integer word problems with confidence. We'll explore various problem types, provide step-by-step solutions, and offer tips and tricks to enhance your problem-solving abilities.

Understanding Integers

Before diving into word problems, let's solidify our understanding of integers. Integers are whole numbers that can be positive, negative, or zero. Think of a number line:

• Zero (0): The midpoint of the number line.
• Positive Integers (+): Numbers greater than zero located to the right of zero on the number line (e.g., 1, 2, 3, ...).
• Negative Integers (-): Numbers less than zero located to the left of zero on the number line (e.g., -1, -2, -3, ...).

Key Concepts for Solving Integer Word Problems

Successfully solving integer word problems hinges on a few key concepts:

• Identifying Keywords: Certain words indicate addition or subtraction. Look for words like:

  • Addition: increased by, added to, more than, sum, total, in addition to, combined with.
  • Subtraction: decreased by, subtracted from, less than, difference, minus, reduced by.

• Visualizing the Problem: Drawing a number line or creating a simple diagram can often clarify the problem's context and make it easier to visualize the operations involved.

• Using a Number Line: A number line is an invaluable tool for visualizing integer addition and subtraction. Start at zero, then move right for positive integers and left for negative integers.

• The Importance of Order: Subtraction of integers isn't commutative (order matters). a - b is not the same as b - a. Pay close attention to the order of operations specified in the problem.

Types of Integer Word Problems and Examples

Let's explore various types of integer word problems with detailed solutions.

1. Temperature Changes

Example 1: The temperature at 6:00 AM was -5°C. By noon, the temperature had increased by 12°C. What was the temperature at noon?

Solution:

This problem involves addition. We start with -5°C and add 12°C:

-5°C + 12°C = 7°C

The temperature at noon was 7°C.

Example 2: The temperature was 8°C at 10:00 AM. By evening, the temperature had dropped 15°C. What was the evening temperature?

Solution:

This involves subtraction. We start with 8°C and subtract 15°C:

8°C - 15°C = -7°C

The evening temperature was -7°C.

2. Financial Transactions

Example 3: John had $25 in his bank account. He deposited $10 and then withdrew $18. How much money does John have left?

Solution:

This combines addition and subtraction.

Step 1: Deposit $10: $25 + $10 = $35 Step 2: Withdraw $18: $35 - $18 = $17

John has $17 left in his account.

Example 4: Sarah owed her friend $15. She paid back $8. How much does she still owe?

Solution:

Representing the debt as a negative integer:

-$15 + $8 = -$7

Sarah still owes $7.

3. Elevation Changes

Example 5: A submarine is at a depth of -200 meters. It ascends 75 meters. What is its new depth?

Solution:

Ascending means moving upwards (positive direction).

-200 meters + 75 meters = -125 meters

The submarine's new depth is -125 meters.

Example 6: A climber is at an elevation of 3000 meters. She descends 500 meters and then climbs another 200 meters. What is her final elevation?

Solution:

Step 1: Descent: 3000 meters - 500 meters = 2500 meters Step 2: Ascent: 2500 meters + 200 meters = 2700 meters

Her final elevation is 2700 meters.

4. Game Scores

Example 7: In a game, a player starts with 0 points. They score 15 points, lose 8 points, and then score another 5 points. What is their final score?

Solution:

Step 1: Score 15: 0 + 15 = 15 Step 2: Lose 8: 15 - 8 = 7 Step 3: Score 5: 7 + 5 = 12

Their final score is 12 points.

Example 8: A team starts with 5 points and loses 12 points. What is their new score?

Solution:

5 points - 12 points = -7 points

Their new score is -7 points.

Advanced Integer Word Problems

These examples showcase more complex scenarios requiring careful attention to detail and order of operations.

Example 9: A stock's value increased by $10 on Monday, decreased by $5 on Tuesday, and increased by $8 on Wednesday. If the stock started at $50, what is its value at the end of Wednesday?

Solution:

Step 1: Monday: $50 + $10 = $60 Step 2: Tuesday: $60 - $5 = $55 Step 3: Wednesday: $55 + $8 = $63

The stock's value at the end of Wednesday is $63.

Example 10: A deep-sea explorer descends 1500 meters, ascends 300 meters, and then descends another 800 meters. What is their final depth relative to sea level?

Solution:

Step 1: First descent: 0 - 1500 = -1500 meters Step 2: Ascent: -1500 + 300 = -1200 meters Step 3: Second descent: -1200 - 800 = -2000 meters

Their final depth is -2000 meters (2000 meters below sea level).

Strategies for Success

• Read Carefully: Understand the problem's context before attempting to solve it.
• Break it Down: Divide complex problems into smaller, manageable steps.
• Use Visual Aids: Number lines, diagrams, or tables can make the process clearer.
• Check Your Work: Always verify your answer to ensure its accuracy.
• Practice Regularly: Consistent practice is key to mastering integer word problems.

Conclusion

Adding and subtracting integers is a fundamental skill with far-reaching applications. By understanding the concepts, employing effective strategies, and practicing regularly, you'll become proficient in solving even the most challenging integer word problems. Remember to focus on keywords, visualize the problem, and check your work meticulously. With consistent effort, you'll confidently navigate the world of integer arithmetic. Good luck!