Subtract: $ \frac{5}{8 V^2 W} - \frac{3}{2 V W^3} $ Simplify Your Answer As Much As Possible.

Feb 26, 2025 by ADMIN 94 views

$Subtract: $\frac{5}{8v^2w} - \frac{3}{2vw^3}$ Simplify Your Answer as Much as Possible$

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Introduction

In mathematics, subtracting fractions with different denominators can be a challenging task. However, with the right approach and techniques, it can be simplified to a more manageable form. In this article, we will focus on subtracting the given fraction $\frac{5}{8v^2w} - \frac{3}{2vw^3}$ and simplify our answer as much as possible.

Understanding the Problem

To start, let's break down the given fraction and understand what we are dealing with. We have two fractions: $\frac{5}{8v^2w}$ and $\frac{3}{2vw^3}$ . The first fraction has a denominator of $8v^2w$ , while the second fraction has a denominator of $2vw^3$ . Our goal is to subtract these two fractions and simplify the result.

Finding a Common Denominator

One of the key steps in subtracting fractions is to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. In this case, we need to find the LCM of $8v^2w$ and $2vw^3$ . To do this, we can start by factoring each denominator.

Factoring the Denominators

Let's factor the denominators $8v^2w$ and $2vw^3$ .

$8v^2w = 2^3 \cdot v^2 \cdot w$
$2vw^3 = 2 \cdot v \cdot w^3$

Finding the Least Common Multiple (LCM)

Now that we have factored the denominators, we can find the LCM. The LCM is the product of the highest power of each prime factor that appears in either denominator.

LCM = $2^3 \cdot v^2 \cdot w \cdot v \cdot w^3$
LCM = $2^3 \cdot v^3 \cdot w^4$

Rewriting the Fractions with the Common Denominator

Now that we have found the common denominator, we can rewrite each fraction with the common denominator.

$\frac{5}{8v^2w} = \frac{5 \cdot 2^2 \cdot v \cdot w^3}{2^3 \cdot v^3 \cdot w^4}$
$\frac{3}{2vw^3} = \frac{3 \cdot 2^2 \cdot v^2 \cdot w}{2^3 \cdot v^3 \cdot w^4}$

Subtracting the Fractions

Now that we have rewritten the fractions with the common denominator, we can subtract them.

$\frac{5 \cdot 2^2 \cdot v \cdot w^3}{2^3 \cdot v^3 \cdot w^4} - \frac{3 \cdot 2^2 \cdot v^2 \cdot w}{2^3 \cdot v^3 \cdot w^4}$
$\frac{5 \cdot 2^2 \cdot v \cdot w^3 - 3 \cdot 2^2 \cdot v^2 \cdot w}{2^3 \cdot v^3 \cdot w^4}$

Simplifying the Result

Now that we have subtracted the fractions, we can simplify the result.

$\frac{5 \cdot 2^2 \cdot v \cdot w^3 - 3 \cdot 2^2 \cdot v^2 \cdot w}{2^3 \cdot v^3 \cdot w^4}$
$\frac{20vw^3 - 12v^2w}{8v^3w^4}$

Final Answer

The final answer is $\frac{20vw^3 - 12v^2w}{8v^3w^4}$ .

Conclusion

Subtracting fractions with different denominators can be a challenging task, but with the right approach and techniques, it can be simplified to a more manageable form. In this article, we focused on subtracting the given fraction $\frac{5}{8v^2w} - \frac{3}{2vw^3}$ and simplified our answer as much as possible. We found a common denominator, rewrote the fractions with the common denominator, subtracted the fractions, and simplified the result. The final answer is $\frac{20vw^3 - 12v^2w}{8v^3w^4}$ .

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Introduction

In our previous article, we discussed how to subtract fractions with different denominators. We walked through the steps of finding a common denominator, rewriting the fractions with the common denominator, subtracting the fractions, and simplifying the result. In this article, we will answer some frequently asked questions (FAQs) related to subtracting fractions with different denominators.

Q: What is the first step in subtracting fractions with different denominators?

A: The first step in subtracting fractions with different denominators is to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators.

Q: How do I find the least common multiple (LCM) of two denominators?

A: To find the LCM of two denominators, you can start by factoring each denominator. Then, find the product of the highest power of each prime factor that appears in either denominator.

Q: What if the denominators have different prime factors?

A: If the denominators have different prime factors, you can still find the LCM by multiplying the highest power of each prime factor that appears in either denominator.

Q: Can I always find a common denominator?

A: Yes, you can always find a common denominator. However, the common denominator may be a large number, which can make the fraction more difficult to work with.

Q: How do I rewrite the fractions with the common denominator?

A: To rewrite the fractions with the common denominator, you can multiply the numerator and denominator of each fraction by the necessary factors to obtain the common denominator.

Q: What if I have a fraction with a variable in the denominator?

A: If you have a fraction with a variable in the denominator, you can still find the LCM by factoring the denominator and finding the product of the highest power of each prime factor that appears in the denominator.

Q: Can I simplify the fraction after subtracting the fractions?

A: Yes, you can simplify the fraction after subtracting the fractions by canceling out any common factors in the numerator and denominator.

Q: What if the fraction cannot be simplified?

A: If the fraction cannot be simplified, it is still a valid result. You can leave the fraction in its current form or simplify it further if possible.

Q: Are there any shortcuts for subtracting fractions with different denominators?

A: While there are no shortcuts for subtracting fractions with different denominators, you can use the following tips to make the process easier:

Use a calculator to find the LCM of the two denominators.
Rewrite the fractions with the common denominator by multiplying the numerator and denominator of each fraction by the necessary factors.
Simplify the fraction after subtracting the fractions by canceling out any common factors in the numerator and denominator.

Q: Can I use a calculator to subtract fractions with different denominators?

A: Yes, you can use a calculator to subtract fractions with different denominators. However, keep in mind that the calculator may not always give you the simplest form of the fraction.

Q: Are there any online tools or resources that can help me subtract fractions with different denominators?

A: Yes, there are many online tools and resources that can help you subtract fractions with different denominators. Some popular options include:

Online calculators
Math websites and forums
Educational software and apps

Conclusion

Subtracting fractions with different denominators can be a challenging task, but with the right approach and techniques, it can be simplified to a more manageable form. In this article, we answered some frequently asked questions (FAQs) related to subtracting fractions with different denominators. We hope that this article has provided you with a better understanding of how to subtract fractions with different denominators and has helped you to become more confident in your math skills.