Integer Word Problems Worksheet With Answers Pdf

Integer Word Problems Worksheet with Answers: A Comprehensive Guide

Are you struggling with integer word problems? Do you find yourself getting lost in the negative numbers and struggling to translate word problems into mathematical equations? You're not alone! Many students find integer word problems challenging, but with the right approach and practice, you can master them. This comprehensive guide will provide you with a variety of integer word problems, explain the strategies for solving them, and offer solutions to help you build your confidence and skills. We'll also discuss some key strategies for tackling these problems, covering everything from understanding keywords to checking your answers. Let’s dive in!

Understanding Integers

Before we tackle word problems, let's refresh our understanding of integers. Integers are whole numbers (no fractions or decimals) that can be positive, negative, or zero. Examples include -3, -2, -1, 0, 1, 2, 3, and so on. Understanding the concept of positive and negative numbers is crucial for solving integer word problems. Think of a number line: numbers to the right of zero are positive, and numbers to the left are negative.

Keywords to Look For

Integer word problems often use specific keywords to indicate addition, subtraction, multiplication, or division. Learning to recognize these keywords is the first step towards successfully solving these problems. Here's a helpful list:

Addition Keywords:

• Increased by: "The temperature increased by 5 degrees."
• More than: "She has 10 more apples than him."
• Added to: "5 was added to the account."
• Sum: "Find the sum of -3 and 7."
• Total: "What is the total of all the scores?"
• Combined: "The combined weight of the boxes is 20kg."

Subtraction Keywords:

• Decreased by: "The water level decreased by 2 inches."
• Less than: "He has 5 less than her."
• Subtracted from: "7 is subtracted from 12."
• Difference: "Find the difference between 15 and -5."
• Reduced by: "The price was reduced by 10%."
• Fewer than: "There are 3 fewer birds than yesterday."

Multiplication Keywords:

• Times: "The quantity is three times greater."
• Product: "Find the product of -4 and 6."
• Of: "One-half of the total amount."
• Multiplied by: "The number is multiplied by 5."

Division Keywords:

• Divided by: "The cake is divided by 8 people."
• Quotient: "Find the quotient of 12 and -3."
• Split equally: "The money was split equally among 5 friends."

Strategies for Solving Integer Word Problems

Now that we've covered the basics, let's look at a structured approach to solving integer word problems:

1. Read Carefully: Thoroughly read the problem to understand what is being asked. Identify the known values and the unknown value(s) you need to find.

2. Identify Keywords: Look for keywords that indicate the mathematical operation(s) involved (addition, subtraction, multiplication, or division).

3. Assign Variables: Assign variables (e.g., x, y, z) to represent the unknown values.

4. Translate into an Equation: Translate the word problem into a mathematical equation using the identified keywords and assigned variables.

5. Solve the Equation: Use the order of operations (PEMDAS/BODMAS) to solve the equation and find the value of the unknown variable(s). Remember to follow the rules for integer operations (addition, subtraction, multiplication, and division of positive and negative numbers).

6. Check Your Answer: Verify your answer by substituting it back into the original equation or by re-reading the problem to ensure it makes sense within the context of the problem. Does your answer logically fit the scenario presented?

Example Integer Word Problems with Solutions

Let's work through some examples to solidify these strategies.

Problem 1: The temperature in the morning was -5°C. By noon, it had increased by 8°C. What was the temperature at noon?

Solution:

1. Read Carefully: We know the starting temperature (-5°C) and the increase (8°C). We need to find the temperature at noon.

2. Keywords: "Increased by" indicates addition.

3. Equation: Let 'x' be the temperature at noon. The equation is: -5 + 8 = x

4. Solve: x = 3°C

5. Check: An increase of 8°C from -5°C logically results in a temperature of 3°C.

Problem 2: A submarine is at a depth of -200 meters. It ascends 50 meters. What is its new depth?

Solution:

1. Read Carefully: The submarine starts at -200 meters and ascends (goes up) 50 meters. We need its new depth.

2. Keywords: "Ascends" indicates addition (although it's adding a positive value to a negative value).

3. Equation: Let 'x' be the new depth. The equation is: -200 + 50 = x

4. Solve: x = -150 meters

5. Check: Ascending 50 meters from -200 meters logically results in a depth of -150 meters.

Problem 3: A diver descends 25 meters, then ascends 10 meters, and finally descends another 15 meters. What is the diver's final depth?

Solution:

1. Read Carefully: The diver performs multiple ascents and descents.

2. Keywords: "Descends" indicates subtraction (adding a negative value), and "ascends" indicates addition.

3. Equation: Let 'x' be the final depth. The equation is: -25 + 10 - 15 = x

4. Solve: x = -30 meters

5. Check: The sequence of descents and ascents logically results in a final depth of -30 meters.

Problem 4: A company made a profit of $5000 in January and a loss of $2000 in February. What was the company's overall profit or loss for the two months?

Solution:

1. Read Carefully: Profit is positive, loss is negative.

2. Keywords: Profit and loss indicate addition (with a positive and negative number).

3. Equation: Let 'x' be the overall profit/loss. The equation is: 5000 + (-2000) = x

4. Solve: x = $3000 (profit)

5. Check: A profit of $5000 followed by a loss of $2000 logically results in an overall profit of $3000.

Problem 5: If the product of two integers is -36 and one integer is 9, what is the other integer?

Solution:

1. Read Carefully: We have the product (-36) and one of the integers (9).

2. Keywords: "Product" indicates multiplication.

3. Equation: Let 'x' be the other integer. The equation is: 9 * x = -36

4. Solve: x = -4

5. Check: The product of 9 and -4 is indeed -36.

Advanced Integer Word Problems

Let's explore some more complex scenarios:

Problem 6: Sarah owes her friend $15. She earns $20 doing chores and pays back her friend. How much money does she have left?

Solution:

1. Read Carefully: Debt is represented as a negative number.

2. Equation: -15 + 20 = x

3. Solve: x = $5

4. Check: After earning $20 and paying back $15, she logically has $5 left.

Problem 7: The temperature drops 3 degrees each hour for 5 hours. What is the total temperature change?

Solution:

1. Read Carefully: The temperature change per hour is negative.

2. Equation: -3 * 5 = x

3. Solve: x = -15 degrees

4. Check: Over 5 hours, the 3-degree drop per hour makes sense.

Problem 8: A hiker climbs 100 meters up a mountain, then descends 50 meters, and finally climbs another 75 meters. What is the hiker's final elevation change?

Solution:

1. Read Carefully: Ascents are positive, descents are negative.

2. Equation: 100 + (-50) + 75 = x

3. Solve: x = 125 meters

4. Check: Adding and subtracting the different changes logically brings us to 125 meters.

Creating Your Own Worksheet

Now that you've worked through these examples, you can create your own integer word problem worksheets. Start with simple problems, gradually increasing the difficulty. Remember to include a variety of keywords and scenarios to provide comprehensive practice. You can easily create a PDF worksheet using word processing software or online tools. Always include an answer key for self-checking.

Conclusion

Mastering integer word problems requires practice and a systematic approach. By understanding integers, identifying keywords, and using a step-by-step problem-solving strategy, you can build confidence and improve your skills. Remember to carefully read each problem, translate it into a mathematical equation, solve it, and always check your answer. With consistent practice and the strategies outlined in this guide, you'll be solving integer word problems with ease! Remember to create a variety of problems to challenge yourself and track your progress. Consistent effort and practice will lead you to master this important math skill.