Checking the Reasonableness of the Solution

Oct 13, 2025 by windailys.com 96 views

Reasonableness of Mathematical Solutions: A Guide to Checking Your Work

Mathematics is a field that requires precision and accuracy. When solving equations, it's essential to verify the reasonableness of your answer to ensure that it's correct. In this article, we'll explore how to check the reasonableness of mathematical solutions, using the example of Jin solving the equation ${-225 + (-15)}$ . We'll examine the different methods to verify the solution and provide a step-by-step guide on how to do it.

Jin is solving the equation ${-225 + (-15)}$ . To determine the reasonableness of his answer, he needs to verify that his solution is correct. The equation involves subtracting two negative numbers, which can be a bit tricky. Let's break it down step by step.

Step 1: Subtracting Negative Numbers

When subtracting two negative numbers, we need to remember that subtracting a negative number is equivalent to adding a positive number. So, in this case, subtracting ${-15}$ is the same as adding ${15}$ .

Step 2: Simplifying the Equation

Now that we've simplified the equation, we can rewrite it as:

${-225 + 15}$

Step 3: Solving the Equation

To solve the equation, we need to subtract ${15}$ from ${-225}$ . This can be done by subtracting ${15}$ from ${-225}$ , which gives us:

${-225 - 15 = -240}$

Checking the Reasonableness of the Solution

Now that we've solved the equation, we need to verify that the solution is reasonable. To do this, we can use the following methods:

Method 1: Checking the Signs

When subtracting two negative numbers, the result is always negative. In this case, the result is ${-240}$ , which is a negative number. This checks out, as we would expect the result to be negative.

Method 2: Checking the Magnitude

The magnitude of the result is also important. In this case, the magnitude of ${-240}$ is ${240}$ . We can check if this is reasonable by comparing it to the original numbers. The original numbers were ${-225}$ and ${-15}$ , which have a magnitude of ${225}$ and ${15}$ , respectively. The result ${-240}$ has a magnitude of ${240}$ , which is greater than the original numbers. This is reasonable, as we would expect the result to be greater than the original numbers.

Method 3: Checking the Reasonableness of the Calculation

We can also check the reasonableness of the calculation by plugging in some values. For example, if we substitute ${-225}$ with ${-200}$ and ${-15}$ with ${-10}$ , we get:

${-200 - 10 = -210}$

This is close to the original result of ${-240}$ , which suggests that the calculation is reasonable.

In conclusion, checking the reasonableness of mathematical solutions is an essential step in ensuring that our answers are correct. By using the methods outlined above, we can verify that our solution is reasonable and accurate. In this article, we've explored how to check the reasonableness of mathematical solutions using the example of Jin solving the equation ${-225 + (-15)}$ . We've examined the different methods to verify the solution and provided a step-by-step guide on how to do it.

The final answer is:

A. Dividing ${-25}$ by ${-10}$ : This is not the correct answer, as dividing two negative numbers will result in a positive number.
B. Multiplying ${-25}$ by ${-10}$ : This is not the correct answer, as multiplying two negative numbers will result in a positive number.
C. Dividing ${-25}$ by ${-10}$ : This is the correct answer, as dividing two negative numbers will result in a positive number.

Note: The correct answer is C. Dividing ${-25}$ by ${-10}$ , but the question is asking which solution would help Jin determine the reasonableness of his answer. The correct solution is actually the one that involves checking the reasonableness of the calculation, which is not listed as an option.
Reasonableness of Mathematical Solutions: A Guide to Checking Your Work

In our previous article, we explored how to check the reasonableness of mathematical solutions using the example of Jin solving the equation ${-225 + (-15)}$ . We examined the different methods to verify the solution and provided a step-by-step guide on how to do it. In this article, we'll answer some frequently asked questions about checking the reasonableness of mathematical solutions.

Q: What is the purpose of checking the reasonableness of mathematical solutions?

A: The purpose of checking the reasonableness of mathematical solutions is to ensure that our answers are correct and accurate. By verifying the reasonableness of our solutions, we can catch any mistakes or errors that may have occurred during the calculation.

Q: How do I check the reasonableness of my solution?

A: There are several methods to check the reasonableness of your solution, including:

Checking the signs of the numbers involved in the calculation
Checking the magnitude of the numbers involved in the calculation
Checking the reasonableness of the calculation by plugging in some values

Q: What is the difference between checking the signs and checking the magnitude of the numbers involved in the calculation?

A: Checking the signs of the numbers involved in the calculation involves verifying that the result is consistent with the signs of the original numbers. Checking the magnitude of the numbers involved in the calculation involves verifying that the result is consistent with the magnitude of the original numbers.

Q: How do I check the reasonableness of the calculation by plugging in some values?

A: To check the reasonableness of the calculation by plugging in some values, you can substitute some of the original numbers with different values and see if the result is still reasonable. For example, if you're solving the equation ${-225 + (-15)}$ , you can substitute ${-225}$ with ${-200}$ and ${-15}$ with ${-10}$ and see if the result is still reasonable.

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

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

Not checking the signs of the numbers involved in the calculation
Not checking the magnitude of the numbers involved in the calculation
Not checking the reasonableness of the calculation by plugging in some values
Not using a calculator or computer to check the reasonableness of the solution

Q: How can I use technology to check the reasonableness of mathematical solutions?

A: You can use technology such as calculators or computers to check the reasonableness of mathematical solutions. For example, you can use a calculator to check the reasonableness of the solution to an equation, or you can use a computer program to check the reasonableness of the solution to a more complex problem.

Q: What are some real-world applications of checking the reasonableness of mathematical solutions?

A: Some real-world applications of checking the reasonableness of mathematical solutions include:

Checking the reasonableness of financial calculations, such as calculating the cost of a product or the return on investment
Checking the reasonableness of scientific calculations, such as calculating the trajectory of a projectile or the behavior of a complex system
Checking the reasonableness of engineering calculations, such as calculating the stress on a structure or the flow of a fluid

In conclusion, checking the reasonableness of mathematical solutions is an essential step in ensuring that our answers are correct and accurate. By using the methods outlined above, we can verify that our solution is reasonable and accurate. In this article, we've answered some frequently asked questions about checking the reasonableness of mathematical solutions and provided some real-world applications of this concept.

The final answer is:

Checking the signs of the numbers involved in the calculation: This is an essential step in checking the reasonableness of mathematical solutions.
Checking the magnitude of the numbers involved in the calculation: This is an essential step in checking the reasonableness of mathematical solutions.
Checking the reasonableness of the calculation by plugging in some values: This is an essential step in checking the reasonableness of mathematical solutions.
Using technology to check the reasonableness of mathematical solutions: This is a useful tool for checking the reasonableness of mathematical solutions.