Solve Integer Word Problems with Ease and Accuracy

Solving Integer Word Problems: A Step-by-Step Guide

Integer word problems can be challenging, but with a clear understanding of the concepts and a systematic approach, you can solve them with ease and accuracy. In this article, we will walk you through the steps to solve integer word problems, provide examples, and offer tips to help you master this skill.

Understanding Integers

Before diving into word problems, it’s essential to understand what integers are. Integers are whole numbers, either positive, negative, or zero, without a fractional part. Examples of integers include -3, 0, 5, and -12.

Step 1: Read and Understand the Problem

The first step in solving an integer word problem is to read and understand the problem carefully. Read the problem statement multiple times, and make sure you understand what is being asked. Identify the key elements of the problem, such as the variables, constants, and the relationships between them.

Step 2: Identify the Integer Operation

Next, identify the integer operation required to solve the problem. Is it addition, subtraction, multiplication, or division? Look for keywords that indicate the operation, such as “increased by,” “decreased by,” “product of,” or “quotient of.”

Step 3: Represent the Problem Algebraically

Represent the problem algebraically, using variables to represent the unknown values. Use integers to represent the known values. For example, if the problem states “Tom has 5 more than twice the number of books as his friend,” you can represent it algebraically as 2x + 5, where x is the number of books Tom’s friend has.

Step 4: Solve the Equation

Solve the equation by performing the required integer operation. Use the order of operations (PEMDAS) to ensure accuracy. For example, if the equation is 2x + 5 = 11, you can solve for x by subtracting 5 from both sides and then dividing both sides by 2.

Step 5: Check Your Solution

Finally, check your solution by plugging it back into the original equation. Verify that the solution satisfies the conditions of the problem. If it does, you have found the correct solution.

Example Problems

Let’s practice solving integer word problems with a few examples:

Example 1:

A bookshelf has 5 shelves, and each shelf can hold 8 books. If the bookshelf is currently empty, how many books can be placed on it in total?

Solution:

Let x be the total number of books that can be placed on the bookshelf.

x = 5 x 8 x = 40

The bookshelf can hold a total of 40 books.

Example 2:

A bakery sells 250 loaves of bread per day. If they make a profit of $0.50 per loaf, how much profit do they make in a day?

Solution:

Let x be the profit made by the bakery in a day.

x = 250 x 0.50 x = 125

The bakery makes a profit of $125 per day.

Tips and Tricks

Here are some tips and tricks to help you solve integer word problems:

• Read carefully: Read the problem statement multiple times to ensure you understand what is being asked.
• Use keywords: Look for keywords that indicate the operation required to solve the problem.
• Represent algebraically: Represent the problem algebraically, using variables to represent the unknown values.
• Check your solution: Check your solution by plugging it back into the original equation.
• Practice, practice, practice: Practice solving integer word problems to build your skills and confidence.

📝 Note: Always check your solution to ensure accuracy and completeness.

Conclusion

Solving integer word problems requires a systematic approach and attention to detail. By following the steps outlined in this article, you can master the skill of solving integer word problems with ease and accuracy. Remember to read carefully, identify the integer operation, represent the problem algebraically, solve the equation, and check your solution.

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