Simplify: \[$1 \frac{5}{8} \div \frac{5}{8}\$\]

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Introduction

When dealing with fractions and mixed numbers, division can be a bit tricky. In this article, we will explore how to simplify the expression $1 \frac{5}{8} \div \frac{5}{8}$ using the rules of arithmetic operations. We will break down the problem step by step, and by the end of this article, you will have a clear understanding of how to simplify this expression.

Understanding the Problem

The given expression is a division problem involving a mixed number and a fraction. To simplify this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: None
2. Exponents: None
3. Multiplication and Division: Evaluate from left to right
4. Addition and Subtraction: Evaluate from left to right

Converting the Mixed Number to an Improper Fraction

To simplify the expression, we need to convert the mixed number $1 \frac{5}{8}$ to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

To convert a mixed number to an improper fraction, we multiply the denominator by the whole number and add the numerator. Then, we write the result as a fraction with the denominator as the original denominator.

In this case, we have:

$1 \frac{5}{8} = \frac{(8 \times 1) + 5}{8} = \frac{13}{8}$

Inverting the Fraction and Multiplying

Now that we have converted the mixed number to an improper fraction, we can rewrite the expression as:

$\frac{13}{8} \div \frac{5}{8}$

To divide fractions, we invert the second fraction and multiply:

$\frac{13}{8} \div \frac{5}{8} = \frac{13}{8} \times \frac{8}{5}$

Simplifying the Expression

Now that we have multiplied the fractions, we can simplify the expression by canceling out any common factors.

In this case, we have:

$\frac{13}{8} \times \frac{8}{5} = \frac{13 \times 8}{8 \times 5} = \frac{104}{40}$

Reducing the Fraction

To reduce the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that divides both numbers without leaving a remainder.

In this case, the GCD of 104 and 40 is 8. We can divide both numbers by 8 to get:

$\frac{104}{40} = \frac{104 \div 8}{40 \div 8} = \frac{13}{5}$

Conclusion

In this article, we simplified the expression $1 \frac{5}{8} \div \frac{5}{8}$ using the rules of arithmetic operations. We converted the mixed number to an improper fraction, inverted the fraction, multiplied, and simplified the expression. By following these steps, we arrived at the final answer of $\frac{13}{5}$.

Frequently Asked Questions

• Q: What is the order of operations? A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the denominator by the whole number and add the numerator. Then, write the result as a fraction with the denominator as the original denominator.
• Q: How do I divide fractions? A: To divide fractions, invert the second fraction and multiply.

Final Answer

The final answer is $\boxed{\frac{13}{5}}$.

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Introduction

In our previous article, we simplified the expression $1 \frac{5}{8} \div \frac{5}{8}$ using the rules of arithmetic operations. We converted the mixed number to an improper fraction, inverted the fraction, multiplied, and simplified the expression. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is the order of operations?

A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the denominator by the whole number and add the numerator. Then, write the result as a fraction with the denominator as the original denominator.

Q: How do I divide fractions?

A: To divide fractions, invert the second fraction and multiply.

Q: What is the difference between a fraction and a mixed number?

A: A fraction is a number that represents a part of a whole, and it is written in the form of a/b, where a is the numerator and b is the denominator. A mixed number is a combination of a whole number and a fraction, and it is written in the form of a b/c, where a is the whole number and b/c is the fraction.

Q: How do I simplify a fraction?

A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator. Then, divide both numbers by the GCD to get the simplified fraction.

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

A: The greatest common divisor (GCD) is the largest number that divides both numbers without leaving a remainder.

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

A: To find the GCD of two numbers, list the factors of each number and find the largest factor that they have in common.

Q: What is the difference between a proper fraction and an improper fraction?

A: A proper fraction is a fraction where the numerator is less than the denominator, and an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, divide the numerator by the denominator and write the result as a whole number and a fraction.

Q: What is the final answer to the expression $1 \frac{5}{8} \div \frac{5}{8}$?

A: The final answer to the expression $1 \frac{5}{8} \div \frac{5}{8}$ is $\boxed{\frac{13}{5}}$.

Conclusion

In this article, we answered some frequently asked questions related to the topic of simplifying the expression $1 \frac{5}{8} \div \frac{5}{8}$. We covered topics such as the order of operations, converting mixed numbers to improper fractions, dividing fractions, and simplifying fractions. By following these steps, you can simplify any expression involving fractions and mixed numbers.

Final Answer

The final answer is $\boxed{\frac{13}{5}}$.