Simplify The Following Expression: 24 2 + 3 8 × 16 2 10 3 ÷ 2 4 \frac{\frac{24}{2}+\frac{3}{8} \times \frac{16}{2}}{\frac{10}{3} \div \frac{2}{4}} 3 10 ​ ÷ 4 2 ​ 2 24 ​ + 8 3 ​ × 2 16 ​ ​

Introduction

Mathematical expressions can be complex and challenging to simplify. In this article, we will focus on simplifying a given mathematical expression that involves fractions, addition, subtraction, multiplication, and division. The expression is $\frac{\frac{24}{2}+\frac{3}{8} \times \frac{16}{2}}{\frac{10}{3} \div \frac{2}{4}}$. We will break down the expression step by step and simplify it to its simplest form.

Step 1: Simplify the Numerator

The numerator of the given expression is $\frac{24}{2}+\frac{3}{8} \times \frac{16}{2}$. To simplify the numerator, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses: $\frac{24}{2}$ and $\frac{16}{2}$ can be simplified to $12$ and $8$ respectively.
2. Multiply the fractions: $\frac{3}{8} \times \frac{16}{2}$ can be simplified to $\frac{3 \times 16}{8 \times 2}$, which is equal to $\frac{48}{16}$.
3. Add the fractions: $\frac{48}{16}$ can be simplified to $3$.

So, the simplified numerator is $12 + 3$, which is equal to $15$.

Step 2: Simplify the Denominator

The denominator of the given expression is $\frac{10}{3} \div \frac{2}{4}$. To simplify the denominator, we need to follow the order of operations (PEMDAS):

1. Invert the second fraction and multiply: $\frac{10}{3} \div \frac{2}{4}$ can be simplified to $\frac{10}{3} \times \frac{4}{2}$.
2. Multiply the fractions: $\frac{10}{3} \times \frac{4}{2}$ can be simplified to $\frac{10 \times 4}{3 \times 2}$, which is equal to $\frac{40}{6}$.
3. Simplify the fraction: $\frac{40}{6}$ can be simplified to $\frac{20}{3}$.

So, the simplified denominator is $\frac{20}{3}$.

Step 3: Simplify the Expression

Now that we have simplified the numerator and denominator, we can simplify the expression:

$\frac{\frac{24}{2}+\frac{3}{8} \times \frac{16}{2}}{\frac{10}{3} \div \frac{2}{4}} = \frac{15}{\frac{20}{3}}$

To simplify the expression, we can multiply the numerator by the reciprocal of the denominator:

$\frac{15}{\frac{20}{3}} = 15 \times \frac{3}{20}$

Simplify the Fraction

To simplify the fraction, we can multiply the numerator and denominator by the same number:

$15 \times \frac{3}{20} = \frac{15 \times 3}{20}$

Final Answer

The final answer is $\frac{45}{20}$, which can be simplified to $\frac{9}{4}$.

Conclusion

Introduction

In our previous article, we simplified a given mathematical expression that involved fractions, addition, subtraction, multiplication, and division. The expression was $\frac{\frac{24}{2}+\frac{3}{8} \times \frac{16}{2}}{\frac{10}{3} \div \frac{2}{4}}$. We broke down the expression step by step and simplified it to its simplest form. In this article, we will answer some frequently asked questions related to the simplification of the given expression.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify a fraction?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. We can then divide both the numerator and denominator by the GCD to simplify the fraction.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Q: How do I add or subtract fractions?

A: To add or subtract fractions, we need to have the same denominator. We can then add or subtract the numerators and keep the same denominator.

Q: How do I multiply or divide fractions?

A: To multiply or divide fractions, we can multiply or divide the numerators and denominators separately.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and denominator. For example, the reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$.

Q: How do I simplify a complex fraction?

A: To simplify a complex fraction, we need to follow the order of operations (PEMDAS) and simplify the numerator and denominator separately.

Q: What is the final answer to the given expression?

A: The final answer to the given expression is $\frac{9}{4}$.

Conclusion

In this article, we answered some frequently asked questions related to the simplification of the given mathematical expression. We covered topics such as the order of operations (PEMDAS), simplifying fractions, adding and subtracting fractions, multiplying and dividing fractions, and simplifying complex fractions. We hope that this article has been helpful in understanding the simplification of the given expression.

Additional Resources

For more information on simplifying mathematical expressions, we recommend the following resources:

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions

Final Thoughts

Simplifying mathematical expressions can be challenging, but with practice and patience, it can become easier. We hope that this article has been helpful in understanding the simplification of the given expression. If you have any further questions or need additional help, please don't hesitate to ask.