Multiplying Each Term by a Suitable Number

Oct 13, 2025 by magicalceylontours.com 102 views

Introduction

When solving equations, it's often helpful to eliminate decimals to make calculations easier and more accurate. In this article, we'll explore how to eliminate decimals in equations by multiplying each term by a suitable number. We'll use a specific equation as an example to demonstrate the process.

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 before solving for $m$ . To do this, we need to find a number that can be multiplied by each term to make the decimals disappear.

Multiplying Each Term by a Suitable Number

To eliminate the decimals, we need to find a number that can be multiplied by each term to make the decimals disappear. Let's analyze each term in the equation:

$-m$ : This term is already in integer form, so we don't need to multiply it by anything.
$0.02$ : This term has a decimal value of $0.02$ . To eliminate the decimal, we can multiply it by $100$ , which is the smallest number that will make the decimal disappear.
$2.1m$ : This term has a decimal value of $2.1$ . To eliminate the decimal, we can multiply it by $10$ , which is the smallest number that will make the decimal disappear.
$-1.45$ : This term has a decimal value of $-1.45$ . To eliminate the decimal, we can multiply it by $100$ , which is the smallest number that will make the decimal disappear.
$-4.81m$ : This term has a decimal value of $-4.81$ . To eliminate the decimal, we can multiply it by $10$ , which is the smallest number that will make the decimal disappear.

Choosing the Correct Number

Now that we've analyzed each term, we need to choose the correct number to multiply each term by. Based on our analysis, we can see that the correct numbers are:

$0.02$ should be multiplied by $100$
$2.1m$ should be multiplied by $10$
$-1.45$ should be multiplied by $100$
$-4.81m$ should be multiplied by $10$

However, we can simplify the process by choosing a common multiple for all terms. In this case, the common multiple is $100$ , so we can multiply each term by $100$ .

Multiplying Each Term by 100

Let's multiply each term by $100$ :

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

Now that we've eliminated the decimals, we can solve for $m$ .

Solving for m

To solve for $m$ , we can start by combining like terms:

-100m + 210m = -481m

110m = -481m

Next, we can add $481m$ to both sides of the equation:

110m + 481m = -481m + 481m

591m = 0

Finally, we can divide both sides of the equation by $591$ to solve for $m$ :

m = \frac{0}{591}

m = 0

Conclusion

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

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

Q: How do I know which number to multiply each term by to eliminate decimals?

A: To determine which number to multiply each term by, you need to analyze each term in the equation. Look for the decimal value in each term and choose the smallest number that will make the decimal disappear. In some cases, you may need to choose a common multiple for all terms.

Q: Can I multiply each term by any number to eliminate decimals?

A: No, you cannot multiply each term by any number to eliminate decimals. You need to choose a number that will make the decimal disappear without changing the value of the term. For example, if a term has a decimal value of $0.02$ , you can multiply it by $100$ to eliminate the decimal, but you cannot multiply it by $50$ or $200$ .

Q: How do I know if I have chosen the correct number to multiply each term by?

A: To determine if you have chosen the correct number to multiply each term by, you can check the equation after multiplying each term. If the decimals have disappeared and the equation is simplified, then you have chosen the correct number.

Q: Can I use a calculator to eliminate decimals in equations?

A: Yes, you can use a calculator to eliminate decimals in equations. However, it's often more helpful to understand the process of eliminating decimals by hand, as this can help you to better understand the underlying math and make calculations more accurate.

Q: Are there any other ways to eliminate decimals in equations besides multiplying each term by a number?

A: Yes, there are other ways to eliminate decimals in equations besides multiplying each term by a number. For example, you can use algebraic manipulations, such as adding or subtracting terms, to eliminate decimals. However, multiplying each term by a number is often the simplest and most straightforward method.

Q: Can I eliminate decimals in equations with fractions?

A: Yes, you can eliminate decimals in equations with fractions. To do this, you need to convert the fractions to decimals and then multiply each term by a number to eliminate the decimals.

Q: Are there any specific rules or formulas for eliminating decimals in equations?

A: There are no specific rules or formulas for eliminating decimals in equations. The process of eliminating decimals is based on understanding the underlying math and choosing the correct number to multiply each term by.

Q: Can I use a computer program or software to eliminate decimals in equations?

A: Yes, you can use a computer program or software to eliminate decimals in equations. Many math software programs, such as Mathematica or Maple, have built-in functions for eliminating decimals in equations.

Q: Are there any limitations to eliminating decimals in equations?

A: Yes, there are limitations to eliminating decimals in equations. For example, if an equation has a large number of terms or complex algebraic expressions, it may be difficult or impossible to eliminate decimals using the method of multiplying each term by a number. In such cases, other methods, such as algebraic manipulations or numerical methods, may be more effective.