Reformat The Following Mathematical Expression.${ \frac{1}{8} \div 5 = }$ { \frac{1}{8} \times \frac{1}{5} = \}

Introduction to Mathematical Operations

Mathematics is a fundamental subject that deals with numbers, quantities, and shapes. It involves various operations such as addition, subtraction, multiplication, and division. In this article, we will focus on reformatting a mathematical expression involving division and multiplication.

Understanding the Given Expression

The given mathematical expression is $\frac{1}{8} \div 5$. This expression involves division, where $\frac{1}{8}$ is divided by 5. However, the expression is incomplete, and we need to reformat it to make it clear and understandable.

Reformatting the Expression

To reformat the expression, we need to follow the order of operations (PEMDAS). The order of operations states that we need to perform operations in the following order:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

In this case, we have a division operation, which needs to be performed first. However, the expression is incomplete, and we need to add the result of the division operation to make it clear.

Reformatting the Expression with Multiplication

The given expression can be reformed as follows:

$\frac{1}{8} \div 5 = \frac{1}{8} \times \frac{1}{5}$

This expression involves multiplication, where $\frac{1}{8}$ is multiplied by $\frac{1}{5}$. To perform this operation, we need to multiply the numerators and denominators separately.

Multiplying Numerators and Denominators

To multiply fractions, we need to multiply the numerators and denominators separately. In this case, we have:

$\frac{1}{8} \times \frac{1}{5} = \frac{1 \times 1}{8 \times 5}$

Simplifying the Expression

To simplify the expression, we need to multiply the numerators and denominators separately. In this case, we have:

$\frac{1 \times 1}{8 \times 5} = \frac{1}{40}$

Conclusion

In conclusion, the reformed mathematical expression is $\frac{1}{8} \div 5 = \frac{1}{40}$. This expression involves division and multiplication, and we need to follow the order of operations to perform these operations.

Importance of Following the Order of Operations

Following the order of operations is crucial in mathematics. It helps us to perform operations in the correct order and avoid errors. In this case, we need to perform the division operation first and then multiply the result by $\frac{1}{5}$.

Real-World Applications of Mathematical Operations

Mathematical operations such as division and multiplication have numerous real-world applications. For example, in finance, we need to perform division and multiplication operations to calculate interest rates and investment returns. In science, we need to perform these operations to calculate distances and velocities.

Tips for Performing Mathematical Operations

Here are some tips for performing mathematical operations:

• Follow the order of operations: This is crucial in mathematics. We need to perform operations in the correct order to avoid errors.
• Use parentheses: Parentheses help us to group numbers and operations together, making it easier to perform operations.
• Simplify expressions: Simplifying expressions helps us to avoid errors and make calculations easier.
• Check your work: Checking our work is crucial in mathematics. We need to verify our answers to ensure that they are correct.

Common Mistakes in Mathematical Operations

Here are some common mistakes in mathematical operations:

• Not following the order of operations: This is a common mistake in mathematics. We need to perform operations in the correct order to avoid errors.
• Not using parentheses: Parentheses help us to group numbers and operations together, making it easier to perform operations.
• Not simplifying expressions: Simplifying expressions helps us to avoid errors and make calculations easier.
• Not checking our work: Checking our work is crucial in mathematics. We need to verify our answers to ensure that they are correct.

Conclusion

In conclusion, reformatting the given mathematical expression involves following the order of operations and performing division and multiplication operations. We need to simplify the expression and check our work to ensure that the answer is correct. By following these tips and avoiding common mistakes, we can perform mathematical operations with confidence and accuracy.

Final Answer

The final answer is $\boxed{\frac{1}{40}}$.

Introduction to Mathematical Operations

Mathematics is a fundamental subject that deals with numbers, quantities, and shapes. It involves various operations such as addition, subtraction, multiplication, and division. In this article, we will focus on reformatting a mathematical expression involving division and multiplication.

Q&A: Reformatting the Mathematical Expression

Q: What is the given mathematical expression?

A: The given mathematical expression is $\frac{1}{8} \div 5$.

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics is:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Q: How do we reformat the given expression?

A: To reformat the expression, we need to follow the order of operations. In this case, we have a division operation, which needs to be performed first. However, the expression is incomplete, and we need to add the result of the division operation to make it clear.

Q: How do we perform the division operation?

A: To perform the division operation, we need to divide $\frac{1}{8}$ by 5. This can be written as:

$\frac{1}{8} \div 5 = \frac{1}{8} \times \frac{1}{5}$

Q: How do we multiply fractions?

A: To multiply fractions, we need to multiply the numerators and denominators separately. In this case, we have:

$\frac{1}{8} \times \frac{1}{5} = \frac{1 \times 1}{8 \times 5}$

Q: How do we simplify the expression?

A: To simplify the expression, we need to multiply the numerators and denominators separately. In this case, we have:

$\frac{1 \times 1}{8 \times 5} = \frac{1}{40}$

Q: What is the final answer?

A: The final answer is $\boxed{\frac{1}{40}}$.

Common Questions and Answers

Q: What is the difference between division and multiplication?

A: Division and multiplication are two different operations in mathematics. Division involves dividing one number by another, while multiplication involves multiplying two numbers together.

Q: How do we perform division with fractions?

A: To perform division with fractions, we need to follow the order of operations. In this case, we have a division operation, which needs to be performed first. However, the expression is incomplete, and we need to add the result of the division operation to make it clear.

Q: How do we perform multiplication with fractions?

A: To perform multiplication with fractions, we need to multiply the numerators and denominators separately. In this case, we have:

$\frac{1}{8} \times \frac{1}{5} = \frac{1 \times 1}{8 \times 5}$

Q: How do we simplify expressions with fractions?

A: To simplify expressions with fractions, we need to multiply the numerators and denominators separately. In this case, we have:

$\frac{1 \times 1}{8 \times 5} = \frac{1}{40}$

Tips for Performing Mathematical Operations

Here are some tips for performing mathematical operations:

• Follow the order of operations: This is crucial in mathematics. We need to perform operations in the correct order to avoid errors.
• Use parentheses: Parentheses help us to group numbers and operations together, making it easier to perform operations.
• Simplify expressions: Simplifying expressions helps us to avoid errors and make calculations easier.
• Check your work: Checking our work is crucial in mathematics. We need to verify our answers to ensure that they are correct.

Common Mistakes in Mathematical Operations

Here are some common mistakes in mathematical operations:

• Not following the order of operations: This is a common mistake in mathematics. We need to perform operations in the correct order to avoid errors.
• Not using parentheses: Parentheses help us to group numbers and operations together, making it easier to perform operations.
• Not simplifying expressions: Simplifying expressions helps us to avoid errors and make calculations easier.
• Not checking our work: Checking our work is crucial in mathematics. We need to verify our answers to ensure that they are correct.

Conclusion

In conclusion, reformatting the given mathematical expression involves following the order of operations and performing division and multiplication operations. We need to simplify the expression and check our work to ensure that the answer is correct. By following these tips and avoiding common mistakes, we can perform mathematical operations with confidence and accuracy.

Final Answer

The final answer is $\boxed{\frac{1}{40}}$.