Simplify The Expression: ${ \frac{8k+9}{18} - \frac{2k+1}{18} }$

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Introduction

Algebraic manipulation is a crucial aspect of mathematics, and simplifying expressions is an essential skill that every student should master. In this article, we will focus on simplifying the given expression: 8k+918−2k+118\frac{8k+9}{18} - \frac{2k+1}{18}. We will break down the problem into manageable steps, and by the end of this article, you will have a clear understanding of how to simplify complex algebraic expressions.

Understanding the Problem

The given expression is a combination of two fractions, and our goal is to simplify it. To do this, we need to first understand the concept of combining like terms and simplifying fractions. Let's start by analyzing the given expression:

8k+918−2k+118\frac{8k+9}{18} - \frac{2k+1}{18}

Step 1: Identify Like Terms

The first step in simplifying the expression is to identify like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable kk raised to the power of 1. We can rewrite the expression as:

8k18+918−2k18−118\frac{8k}{18} + \frac{9}{18} - \frac{2k}{18} - \frac{1}{18}

Step 2: Combine Like Terms

Now that we have identified like terms, we can combine them. We can combine the terms with the variable kk and the constant terms separately. Let's start by combining the terms with the variable kk:

8k18−2k18\frac{8k}{18} - \frac{2k}{18}

We can simplify this expression by combining the numerators:

6k18\frac{6k}{18}

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression further. We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 6 and 18 is 6. Let's simplify the fraction:

6k18=k3\frac{6k}{18} = \frac{k}{3}

Step 4: Simplify the Constant Terms

We still have the constant terms to simplify. We can combine the constant terms as follows:

918−118\frac{9}{18} - \frac{1}{18}

We can simplify this expression by combining the numerators:

818\frac{8}{18}

Step 5: Simplify the Constant Terms Further

We can simplify the fraction further by dividing both the numerator and the denominator by their GCD. In this case, the GCD of 8 and 18 is 2. Let's simplify the fraction:

818=49\frac{8}{18} = \frac{4}{9}

Step 6: Combine the Simplified Terms

Now that we have simplified the terms with the variable kk and the constant terms, we can combine them. Let's rewrite the expression as:

k3+49\frac{k}{3} + \frac{4}{9}

Step 7: Simplify the Expression Further

We can simplify the expression further by finding a common denominator. In this case, the common denominator is 9. Let's rewrite the expression as:

3k9+49\frac{3k}{9} + \frac{4}{9}

Step 8: Combine the Terms

Now that we have a common denominator, we can combine the terms. Let's rewrite the expression as:

3k+49\frac{3k+4}{9}

Conclusion

In this article, we have simplified the given expression: 8k+918−2k+118\frac{8k+9}{18} - \frac{2k+1}{18}. We have broken down the problem into manageable steps, and by the end of this article, you should have a clear understanding of how to simplify complex algebraic expressions. Remember to identify like terms, combine them, and simplify the expression further by finding a common denominator.

Final Answer

The final answer is: 3k+49\boxed{\frac{3k+4}{9}}

Frequently Asked Questions

  • Q: What is the first step in simplifying the expression? A: The first step in simplifying the expression is to identify like terms.
  • Q: How do I combine like terms? A: You can combine like terms by adding or subtracting the coefficients of the terms with the same variable raised to the same power.
  • Q: How do I simplify a fraction? A: You can simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  • Q: What is the final answer? A: The final answer is: 3k+49\boxed{\frac{3k+4}{9}}

Introduction

In our previous article, we simplified the expression: 8k+918−2k+118\frac{8k+9}{18} - \frac{2k+1}{18}. We broke down the problem into manageable steps and provided a clear understanding of how to simplify complex algebraic expressions. In this article, we will provide a Q&A section to address any questions or concerns you may have.

Q&A

Q: What is the first step in simplifying the expression?

A: The first step in simplifying the expression is to identify like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: You can combine like terms by adding or subtracting the coefficients of the terms with the same variable raised to the same power. For example, in the expression 8k18−2k18\frac{8k}{18} - \frac{2k}{18}, you can combine the terms by adding the coefficients: 8k18−2k18=6k18\frac{8k}{18} - \frac{2k}{18} = \frac{6k}{18}.

Q: How do I simplify a fraction?

A: You can simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). For example, in the expression 6k18\frac{6k}{18}, you can simplify the fraction by dividing both the numerator and the denominator by 6: 6k18=k3\frac{6k}{18} = \frac{k}{3}.

Q: What is the final answer?

A: The final answer is: 3k+49\boxed{\frac{3k+4}{9}}.

Q: Can I simplify the expression further?

A: Yes, you can simplify the expression further by finding a common denominator. In this case, the common denominator is 9. Let's rewrite the expression as: 3k9+49\frac{3k}{9} + \frac{4}{9}. Now, you can combine the terms: 3k+49\frac{3k+4}{9}.

Q: How do I know when to simplify an expression?

A: You should simplify an expression when it is necessary to make the expression easier to work with. For example, if you are solving an equation, you may need to simplify the expression to isolate the variable.

Q: Can I use a calculator to simplify an expression?

A: Yes, you can use a calculator to simplify an expression. However, it is always a good idea to check your work by hand to make sure you understand the steps involved in simplifying the expression.

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

A: Some common mistakes to avoid when simplifying an expression include:

  • Not identifying like terms
  • Not combining like terms correctly
  • Not simplifying the fraction correctly
  • Not finding a common denominator when necessary

Conclusion

In this article, we have provided a Q&A section to address any questions or concerns you may have about simplifying the expression: 8k+918−2k+118\frac{8k+9}{18} - \frac{2k+1}{18}. We have covered topics such as identifying like terms, combining like terms, simplifying fractions, and finding a common denominator. Remember to always check your work by hand to make sure you understand the steps involved in simplifying the expression.

Final Answer

The final answer is: 3k+49\boxed{\frac{3k+4}{9}}

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