Jin Solves The Equation { -225 \div (-15)$}$. Which Solution Would Help Jin Determine The Reasonableness Of His Answer?A. Dividing { -25$}$ By { -10$}$B. Multiplying { -25$}$ By { -10$}$C. Dividing

Mar 8, 2025 by ADMIN 198 views

**Reasonableness of Mathematical Solutions: A Case Study**

Introduction

In mathematics, solving equations is a fundamental concept that requires not only technical proficiency but also critical thinking and problem-solving skills. One of the essential aspects of mathematical problem-solving is verifying the reasonableness of the solution obtained. This involves checking whether the answer makes sense in the context of the problem and is consistent with the given information. In this article, we will explore how Jin can determine the reasonableness of his answer to the equation ${-225 \div (-15)}$ .

Understanding the Problem

Jin is faced with the task of solving the equation ${-225 \div (-15)}$ . To solve this equation, Jin needs to perform division, which involves finding the quotient of two numbers. In this case, the dividend is ${-225}$ and the divisor is ${-15}$ . To find the quotient, Jin will divide the dividend by the divisor.

Reasonableness of the Solution

To determine the reasonableness of Jin's answer, he needs to perform a sanity check. This involves verifying whether the solution makes sense in the context of the problem. One way to do this is to check if the solution is consistent with the given information. In this case, the given information is the dividend and the divisor.

Option A: Dividing ${-25}$ by ${-10}$

Option A involves dividing ${-25}$ by ${-10}$ . This is a simple division problem that can be solved by dividing the absolute values of the numbers and then applying the correct sign to the result. The absolute value of ${-25}$ is ${25}$ and the absolute value of ${-10}$ is ${10}$ . Dividing ${25}$ by ${10}$ gives ${2.5}$ . Since both numbers have the same sign (negative), the result is also negative, which gives ${-2.5}$ .

Option B: Multiplying ${-25}$ by ${-10}$

Option B involves multiplying ${-25}$ by ${-10}$ . This is a simple multiplication problem that can be solved by multiplying the absolute values of the numbers and then applying the correct sign to the result. The absolute value of ${-25}$ is ${25}$ and the absolute value of ${-10}$ is ${10}$ . Multiplying ${25}$ by ${10}$ gives ${250}$ . Since both numbers have the same sign (negative), the result is also negative, which gives ${-250}$ .

Option C: Dividing ${-225}$ by ${-15}$

Option C involves dividing ${-225}$ by ${-15}$ . This is the original equation that Jin needs to solve. To solve this equation, Jin will divide the dividend by the divisor.

Comparing the Options

Now that we have explored the three options, let's compare them to determine which one would help Jin determine the reasonableness of his answer. Option A involves dividing ${-25}$ by ${-10}$ , which gives ${-2.5}$ . Option B involves multiplying ${-25}$ by ${-10}$ , which gives ${-250}$ . Option C involves dividing ${-225}$ by ${-15}$ , which is the original equation that Jin needs to solve.

Conclusion

In conclusion, to determine the reasonableness of Jin's answer to the equation ${-225 \div (-15)}$ , he needs to perform a sanity check. One way to do this is to check if the solution is consistent with the given information. Option C, which involves dividing ${-225}$ by ${-15}$ , is the most relevant option because it is the original equation that Jin needs to solve. By comparing the result of Option C with the result of Option A or Option B, Jin can determine the reasonableness of his answer.

Recommendation

Based on the analysis above, we recommend that Jin perform Option C, which involves dividing ${-225}$ by ${-15}$ . This will give Jin the solution to the original equation and allow him to determine the reasonableness of his answer.

Final Thoughts

In conclusion, determining the reasonableness of a mathematical solution is an essential aspect of problem-solving. By performing a sanity check and comparing the result with the given information, Jin can ensure that his answer is correct and makes sense in the context of the problem. We hope that this article has provided valuable insights and guidance for Jin and other students who are struggling with mathematical problem-solving.

Additional Tips

Here are some additional tips that may help Jin and other students who are struggling with mathematical problem-solving:

Always read the problem carefully and understand what is being asked.
Identify the key elements of the problem, such as the dividend and the divisor.
Perform a sanity check by comparing the result with the given information.
Use visual aids, such as diagrams or charts, to help illustrate the problem and the solution.
Practice, practice, practice! The more you practice, the more confident you will become in your ability to solve mathematical problems.

References

Mathematics textbook
Online math resources
Mathematical problem-solving strategies
Frequently Asked Questions: Reasonableness of Mathematical Solutions ====================================================================

Q: What is the reasonableness of a mathematical solution?

A: The reasonableness of a mathematical solution refers to whether the answer makes sense in the context of the problem and is consistent with the given information.

Q: Why is it important to check the reasonableness of a mathematical solution?

A: Checking the reasonableness of a mathematical solution is essential because it helps to ensure that the answer is correct and makes sense in the context of the problem. This is particularly important in real-world applications where mathematical solutions are used to make decisions or predictions.

Q: How can I determine the reasonableness of a mathematical solution?

A: To determine the reasonableness of a mathematical solution, you can perform a sanity check by comparing the result with the given information. You can also use visual aids, such as diagrams or charts, to help illustrate the problem and the solution.

Q: What are some common mistakes to avoid when checking the reasonableness of a mathematical solution?

A: Some common mistakes to avoid when checking the reasonableness of a mathematical solution include:

Not reading the problem carefully and understanding what is being asked
Not identifying the key elements of the problem, such as the dividend and the divisor
Not performing a sanity check by comparing the result with the given information
Not using visual aids, such as diagrams or charts, to help illustrate the problem and the solution

Q: How can I practice checking the reasonableness of mathematical solutions?

A: You can practice checking the reasonableness of mathematical solutions by working through examples and exercises in a textbook or online resource. You can also try solving real-world problems and checking the reasonableness of your solutions.

Q: What are some additional tips for checking the reasonableness of mathematical solutions?

A: Some additional tips for checking the reasonableness of mathematical solutions include:

Always read the problem carefully and understand what is being asked
Identify the key elements of the problem, such as the dividend and the divisor
Perform a sanity check by comparing the result with the given information
Use visual aids, such as diagrams or charts, to help illustrate the problem and the solution
Practice, practice, practice! The more you practice, the more confident you will become in your ability to solve mathematical problems.

Q: Can you provide some examples of how to check the reasonableness of mathematical solutions?

A: Here are some examples of how to check the reasonableness of mathematical solutions:

Example 1: Solve the equation ${-225 \div (-15)}$ and check the reasonableness of the solution by comparing it with the given information.
Example 2: Solve the equation ${25 \times 10}$ and check the reasonableness of the solution by comparing it with the given information.
Example 3: Solve the equation ${100 \div 10}$ and check the reasonableness of the solution by comparing it with the given information.

Q: How can I apply the concept of reasonableness to real-world problems?

A: You can apply the concept of reasonableness to real-world problems by using mathematical solutions to make decisions or predictions. For example, you can use mathematical solutions to determine the cost of a product, the time it will take to complete a project, or the probability of a certain event occurring.

Q: What are some common applications of the concept of reasonableness in real-world problems?

A: Some common applications of the concept of reasonableness in real-world problems include:

Finance: Using mathematical solutions to determine the cost of a product or the return on investment for a project.
Engineering: Using mathematical solutions to determine the time it will take to complete a project or the probability of a certain event occurring.
Science: Using mathematical solutions to determine the probability of a certain event occurring or the expected value of a random variable.

Q: Can you provide some additional resources for learning more about the concept of reasonableness in mathematical solutions?

A: Here are some additional resources for learning more about the concept of reasonableness in mathematical solutions: