Finding the Multiplying Factor

Oct 13, 2025 by miodeya.com 4 views

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. However, when dealing with decimal numbers, it can be challenging to solve these equations accurately. In this article, we will explore a simple yet effective method to eliminate decimals in linear equations, making it easier to solve them.

Understanding the Problem

The given equation is:

-m + 0.02 + 2.1m = -1.45 - 4.81m

Our goal is to eliminate the decimals in this equation, making it easier to solve for the variable $m$ .

Eliminating Decimals

To eliminate decimals, we need to multiply each term in the equation by a number that will make all the decimals disappear. This number is called the multiplying factor.

Let's analyze the given equation:

The term $-m$ has no decimal.
The term $0.02$ has a decimal of $0.02$ .
The term $2.1m$ has a decimal of $0.1$ .
The term $-1.45$ has a decimal of $0.45$ .
The term $-4.81m$ has a decimal of $0.81$ .

To eliminate the decimals, we need to find a common multiplying factor that will make all the decimals disappear.

Finding the Multiplying Factor

The common multiplying factor is the smallest number that can be multiplied by each term to eliminate the decimals. In this case, the common multiplying factor is 100.

Why 100?

We can multiply each term by 100 to eliminate the decimals:

$-m$ becomes $-100m$
$0.02$ becomes $2$
$2.1m$ becomes $210m$
$-1.45$ becomes $-145$
$-4.81m$ becomes $-481m$

Now, let's rewrite the equation with the multiplied terms:

-100m + 2 + 210m = -145 - 481m

Simplifying the Equation

We can simplify the equation by combining like terms:

110m + 2 = -145 - 481m

Now, let's add $481m$ to both sides of the equation:

110m + 481m + 2 = -145

Combine like terms:

591m + 2 = -145

Subtract 2 from both sides:

591m = -147

Divide both sides by 591:

m = -\frac{147}{591}

Conclusion

In this article, we learned how to eliminate decimals in linear equations by multiplying each term by a common factor. We applied this method to the given equation and solved for the variable $m$ . The common multiplying factor was 100, which eliminated the decimals in the equation.

Answer

The correct answer is:

D. 100

Discussion

This method of eliminating decimals is a simple yet effective way to solve linear equations. By multiplying each term by a common factor, we can make the equation easier to solve. This method is particularly useful when dealing with decimal numbers.

Example Use Cases

This method can be applied to a wide range of linear equations, including those with multiple variables and complex coefficients. Some example use cases include:

Solving systems of linear equations with decimal coefficients
Finding the solution to a linear equation with a decimal constant
Eliminating decimals in a linear equation with multiple variables

Tips and Variations

When dealing with decimal numbers, it's essential to use a common multiplying factor to eliminate the decimals.
The common multiplying factor can be any number that will make all the decimals disappear.
This method can be applied to linear equations with multiple variables and complex coefficients.

Q: What is the purpose of eliminating decimals in linear equations?

A: The purpose of eliminating decimals in linear equations is to make the equation easier to solve. By eliminating decimals, we can simplify the equation and make it more manageable.

Q: How do I eliminate decimals in a linear equation?

A: To eliminate decimals in a linear equation, you need to multiply each term in the equation by a common factor. This common factor is the smallest number that can be multiplied by each term to eliminate the decimals.

Q: What is the common multiplying factor?

A: The common multiplying factor is the smallest number that can be multiplied by each term to eliminate the decimals. In the example we used earlier, the common multiplying factor was 100.

Q: Can I use any number as the common multiplying factor?

A: No, you cannot use any number as the common multiplying factor. The common multiplying factor must be the smallest number that can be multiplied by each term to eliminate the decimals.

Q: How do I know which number to use as the common multiplying factor?

A: To determine which number to use as the common multiplying factor, you need to analyze the equation and identify the smallest number that can be multiplied by each term to eliminate the decimals.

Q: Can I use this method to solve linear equations with multiple variables?

A: Yes, you can use this method to solve linear equations with multiple variables. The process is the same as solving a linear equation with a single variable.

Q: Can I use this method to solve linear equations with complex coefficients?

A: Yes, you can use this method to solve linear equations with complex coefficients. The process is the same as solving a linear equation with real coefficients.

Q: What are some common mistakes to avoid when eliminating decimals in linear equations?

A: Some common mistakes to avoid when eliminating decimals in linear equations include:

Using a number that is not the smallest number that can be multiplied by each term to eliminate the decimals.
Failing to multiply each term by the common multiplying factor.
Not simplifying the equation after eliminating the decimals.

Q: How do I check my work when eliminating decimals in linear equations?

A: To check your work when eliminating decimals in linear equations, you need to:

Verify that you have multiplied each term by the common multiplying factor.
Simplify the equation after eliminating the decimals.
Check that the equation is true for all values of the variable.

Q: What are some real-world applications of eliminating decimals in linear equations?

A: Some real-world applications of eliminating decimals in linear equations include:

Solving systems of linear equations in physics and engineering.
Finding the solution to a linear equation in finance and economics.
Eliminating decimals in a linear equation in computer science and programming.

By following the steps outlined in this article and avoiding common mistakes, you can eliminate decimals in linear equations and make solving them easier.