Not combining the fractions

Oct 13, 2025 by magicalceylontours.com 99 views

$Not combining the fractions$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us to solve problems more efficiently and accurately. When dealing with fractions, simplifying them can make a significant difference in the complexity of the problem. In this article, we will focus on simplifying the expression $\frac{7}{n+9}+\frac{12}{4n+36}$ .

Understanding the Expression

The given expression is a sum of two fractions, each with a different denominator. To simplify this expression, we need to find a common denominator that can be used for both fractions. The common denominator is the least common multiple (LCM) of the two denominators.

Finding the Least Common Multiple (LCM)

To find the LCM of $n+9$ and $4n+36$ , we need to factorize both expressions. We can start by factoring out the greatest common factor (GCF) from each expression.

Factoring Out the GCF

The GCF of $n+9$ is 1, and the GCF of $4n+36$ is 4. We can factor out 4 from the second expression:

4n+36 = 4(n+9)

Now we have:

\frac{7}{n+9}+\frac{12}{4(n+9)}

Simplifying the Expression

Now that we have a common denominator, we can simplify the expression by combining the two fractions.

\frac{7}{n+9}+\frac{12}{4(n+9)} = \frac{7+12}{4(n+9)}

We can simplify the numerator by adding 7 and 12:

\frac{7+12}{4(n+9)} = \frac{19}{4(n+9)}

Simplifying Further

We can simplify the expression further by dividing both the numerator and the denominator by their greatest common factor (GCF). The GCF of 19 and 4 is 1, so we cannot simplify the expression further.

Conclusion

In this article, we simplified the expression $\frac{7}{n+9}+\frac{12}{4n+36}$ by finding the least common multiple (LCM) of the two denominators and combining the two fractions. We then simplified the expression further by dividing both the numerator and the denominator by their greatest common factor (GCF). The simplified expression is $\frac{19}{4(n+9)}$ .

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. In engineering, simplifying expressions can help us to design more efficient systems and solve complex problems. In economics, simplifying expressions can help us to model and analyze complex economic systems.

Tips and Tricks

When simplifying expressions, it's essential to follow these tips and tricks:

Factorize the expression: Factorizing the expression can help us to find the least common multiple (LCM) of the denominators.
Find the greatest common factor (GCF): Finding the GCF of the numerator and the denominator can help us to simplify the expression further.
Combine the fractions: Combining the fractions can help us to simplify the expression and make it easier to work with.

Common Mistakes

When simplifying expressions, it's essential to avoid these common mistakes:

Not finding the least common multiple (LCM): Not finding the LCM of the denominators can make it difficult to simplify the expression.
Not combining the fractions: Not combining the fractions can make the expression more complex and difficult to work with.
Not simplifying further: Not simplifying the expression further can make it more complex and difficult to work with.

Final Thoughts

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. By following the tips and tricks outlined in this article, we can simplify expressions more efficiently and accurately. Remember to factorize the expression, find the greatest common factor (GCF), and combine the fractions to simplify the expression.

Introduction

In our previous article, we simplified the expression $\frac{7}{n+9}+\frac{12}{4n+36}$ by finding the least common multiple (LCM) of the two denominators and combining the two fractions. In this article, we will answer some frequently asked questions (FAQs) about simplifying expressions.

Q&A

Q: What is the least common multiple (LCM) of two numbers?

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

Q: What is the greatest common factor (GCF) of two numbers?

A: The greatest common factor (GCF) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCF of two numbers?

A: To find the GCF of two numbers, you can list the factors of each number and find the largest number that appears in both lists.

Q: What is the difference between the LCM and the GCF?

A: The LCM is the smallest number that is a multiple of both numbers, while the GCF is the largest number that divides both numbers without leaving a remainder.

Q: How do I simplify an expression with multiple fractions?

A: To simplify an expression with multiple fractions, you can find the least common multiple (LCM) of the denominators and combine the fractions.

Q: What is the importance of simplifying expressions?

A: Simplifying expressions is important because it can make the expression easier to work with and can help us to solve problems more efficiently and accurately.

Q: How do I know if an expression can be simplified?

A: An expression can be simplified if it has multiple fractions with different denominators.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include not finding the least common multiple (LCM) of the denominators, not combining the fractions, and not simplifying further.

Tips and Tricks

When simplifying expressions, it's essential to follow these tips and tricks:

Factorize the expression: Factorizing the expression can help us to find the least common multiple (LCM) of the denominators.
Find the greatest common factor (GCF): Finding the GCF of the numerator and the denominator can help us to simplify the expression further.
Combine the fractions: Combining the fractions can help us to simplify the expression and make it easier to work with.
Check for common factors: Checking for common factors can help us to simplify the expression further.

Real-World Applications

Conclusion

In this article, we answered some frequently asked questions (FAQs) about simplifying expressions. We discussed the importance of simplifying expressions, how to find the least common multiple (LCM) and the greatest common factor (GCF), and how to simplify expressions with multiple fractions. We also provided some tips and tricks for simplifying expressions and discussed some common mistakes to avoid.