Simplify The Expression Fully.$\frac{\frac{2}{3}}{\frac{3}{23}+\frac{1}{23}}$

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Introduction

In this article, we will simplify the given expression fully. The expression is 23323+123\frac{\frac{2}{3}}{\frac{3}{23}+\frac{1}{23}}. We will break down the solution into manageable steps, making it easy to understand and follow.

Step 1: Simplify the Denominator

The given expression is 23323+123\frac{\frac{2}{3}}{\frac{3}{23}+\frac{1}{23}}. To simplify this expression, we need to start by simplifying the denominator. The denominator is a sum of two fractions, 323\frac{3}{23} and 123\frac{1}{23}.

# Simplify the Denominator
## Step 1: Find the Common Denominator
The common denominator of $\frac{3}{23}$ and $\frac{1}{23}$ is 23.

## Step 2: Rewrite the Fractions with the Common Denominator
$\frac{3}{23}$ can be rewritten as $\frac{3 \times 1}{23 \times 1} = \frac{3}{23}$.
$\frac{1}{23}$ can be rewritten as $\frac{1 \times 1}{23 \times 1} = \frac{1}{23}$.

## Step 3: Add the Fractions
$\frac{3}{23} + \frac{1}{23} = \frac{3 + 1}{23} = \frac{4}{23}$.

Step 2: Simplify the Expression

Now that we have simplified the denominator, we can simplify the expression. The expression is 23423\frac{\frac{2}{3}}{\frac{4}{23}}.

# Simplify the Expression
## Step 1: Rewrite the Expression
$\frac{\frac{2}{3}}{\frac{4}{23}} = \frac{2}{3} \div \frac{4}{23}$.

## Step 2: Invert and Multiply
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of $\frac{4}{23}$ is $\frac{23}{4}$.
$\frac{2}{3} \div \frac{4}{23} = \frac{2}{3} \times \frac{23}{4}$.

## Step 3: Multiply the Numerators and Denominators
$\frac{2}{3} \times \frac{23}{4} = \frac{2 \times 23}{3 \times 4} = \frac{46}{12}$.

Step 3: Simplify the Result

The expression is now 4612\frac{46}{12}. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

# Simplify the Result
## Step 1: Divide the Numerator and Denominator by 2
$\frac{46}{12} = \frac{46 \div 2}{12 \div 2} = \frac{23}{6}$.

Conclusion

In this article, we simplified the given expression fully. We started by simplifying the denominator, then simplified the expression, and finally simplified the result. The final simplified expression is 236\frac{23}{6}.

Final Answer

Introduction

In our previous article, we simplified the given expression fully. The expression was 23323+123\frac{\frac{2}{3}}{\frac{3}{23}+\frac{1}{23}}. We broke down the solution into manageable steps, making it easy to understand and follow. In this article, we will answer some frequently asked questions related to simplifying the expression fully.

Q&A

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

A: The first step in simplifying the expression is to simplify the denominator. The denominator is a sum of two fractions, 323\frac{3}{23} and 123\frac{1}{23}.

Q: How do I find the common denominator of two fractions?

A: To find the common denominator of two fractions, you need to find the least common multiple (LCM) of the denominators. In this case, the common denominator of 323\frac{3}{23} and 123\frac{1}{23} is 23.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of 423\frac{4}{23} is 234\frac{23}{4}.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 46 and 12 is 2.

Q: What is the final simplified expression?

A: The final simplified expression is 236\frac{23}{6}.

Q: Can I simplify the expression further?

A: Yes, you can simplify the expression further by dividing both the numerator and the denominator by their greatest common divisor (GCD). However, in this case, the GCD of 23 and 6 is 1, so the expression cannot be simplified further.

Q: What is the final answer?

A: The final answer is 236\boxed{\frac{23}{6}}.

Common Mistakes

Mistake 1: Not simplifying the denominator

  • Not simplifying the denominator can lead to a more complex expression.
  • Make sure to simplify the denominator before simplifying the expression.

Mistake 2: Not finding the common denominator

  • Not finding the common denominator can lead to an incorrect expression.
  • Make sure to find the common denominator before simplifying the expression.

Mistake 3: Not simplifying the fraction

  • Not simplifying the fraction can lead to a more complex expression.
  • Make sure to simplify the fraction before finalizing the expression.

Conclusion

In this article, we answered some frequently asked questions related to simplifying the expression fully. We covered topics such as simplifying the denominator, finding the common denominator, simplifying the fraction, and common mistakes to avoid. By following these steps and avoiding common mistakes, you can simplify the expression fully and arrive at the final answer.

Final Answer

The final answer is 236\boxed{\frac{23}{6}}.