Write $\frac{47}{5}$ As A Mixed Number.
Introduction
In mathematics, a mixed number is a combination of a whole number and a proper fraction. It is a way to express a number that is greater than a whole number but less than the next whole number. In this article, we will learn how to write the improper fraction $\frac{47}{5}$ as a mixed number.
What is a Mixed Number?
A mixed number is a combination of a whole number and a proper fraction. It is written in the form $a\frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction part, and $c$ is the denominator of the fraction part. For example, $3\frac{2}{5}$ is a mixed number that represents the number $3$ plus the fraction $\frac{2}{5}$.
Converting an Improper Fraction to a Mixed Number
To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. The quotient will be the whole number part, and the remainder will be the numerator of the fraction part. The denominator of the fraction part will remain the same.
Step-by-Step Procedure
- Divide the numerator by the denominator.
- The quotient will be the whole number part.
- The remainder will be the numerator of the fraction part.
- The denominator of the fraction part will remain the same.
Example
Let's convert the improper fraction $\frac{47}{5}$ to a mixed number using the step-by-step procedure.
- Divide the numerator (47) by the denominator (5).
- The quotient is 9, which will be the whole number part.
- The remainder is 2, which will be the numerator of the fraction part.
- The denominator of the fraction part remains the same, which is 5.
Therefore, the mixed number equivalent of $\frac{47}{5}$ is $9\frac{2}{5}$.
Why is it Important to Convert Improper Fractions to Mixed Numbers?
Converting improper fractions to mixed numbers is an important skill in mathematics because it helps us to:
- Simplify complex fractions
- Perform arithmetic operations with fractions
- Understand the concept of equivalent fractions
- Solve problems in real-world applications
Real-World Applications
Mixed numbers have many real-world applications, such as:
- Measuring lengths and distances
- Calculating areas and volumes
- Solving problems in finance and economics
- Understanding scientific and mathematical concepts
Conclusion
In conclusion, converting an improper fraction to a mixed number is a simple process that involves dividing the numerator by the denominator. The quotient will be the whole number part, and the remainder will be the numerator of the fraction part. The denominator of the fraction part will remain the same. By converting improper fractions to mixed numbers, we can simplify complex fractions, perform arithmetic operations with fractions, and understand the concept of equivalent fractions.
Frequently Asked Questions
Q: What is a mixed number?
A: A mixed number is a combination of a whole number and a proper fraction.
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. The quotient will be the whole number part, and the remainder will be the numerator of the fraction part.
Q: Why is it important to convert improper fractions to mixed numbers?
A: Converting improper fractions to mixed numbers helps us to simplify complex fractions, perform arithmetic operations with fractions, and understand the concept of equivalent fractions.
Q: What are some real-world applications of mixed numbers?
Q: What is a mixed number?
A: A mixed number is a combination of a whole number and a proper fraction. It is written in the form $a\frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction part, and $c$ is the denominator of the fraction part.
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. The quotient will be the whole number part, and the remainder will be the numerator of the fraction part.
Q: What is the difference between an improper fraction and a mixed number?
A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator, while a mixed number is a combination of a whole number and a proper fraction.
Q: Can I simplify a mixed number?
A: Yes, you can simplify a mixed number by dividing the whole number part by the denominator of the fraction part. The result will be a new mixed number with a smaller whole number part.
Q: How do I add or subtract mixed numbers?
A: To add or subtract mixed numbers, you need to follow these steps:
- Add or subtract the whole number parts.
- Add or subtract the fraction parts.
- Combine the results to get the final answer.
Q: Can I multiply or divide mixed numbers?
A: Yes, you can multiply or divide mixed numbers, but you need to follow these steps:
- Multiply or divide the whole number parts.
- Multiply or divide the fraction parts.
- Combine the results to get the final answer.
Q: What are some real-world applications of mixed numbers?
A: Mixed numbers have many real-world applications, such as:
- Measuring lengths and distances
- Calculating areas and volumes
- Solving problems in finance and economics
- Understanding scientific and mathematical concepts
Q: Can I use a calculator to convert an improper fraction to a mixed number?
A: Yes, you can use a calculator to convert an improper fraction to a mixed number. Most calculators have a built-in function to convert fractions to mixed numbers.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, follow these steps:
- Multiply the whole number part by the denominator of the fraction part.
- Add the numerator of the fraction part to the result.
- Write the result as an improper fraction.
Q: Can I simplify a mixed number by canceling out common factors?
A: Yes, you can simplify a mixed number by canceling out common factors between the whole number part and the denominator of the fraction part.
Q: How do I compare two mixed numbers?
A: To compare two mixed numbers, compare the whole number parts first. If the whole number parts are equal, compare the fraction parts. If the fraction parts are equal, the mixed numbers are equal.
Q: Can I use mixed numbers in algebraic expressions?
A: Yes, you can use mixed numbers in algebraic expressions. However, you need to follow the rules of algebra and simplify the expressions as needed.
Q: How do I graph mixed numbers on a number line?
A: To graph mixed numbers on a number line, plot the whole number part on the number line and then plot the fraction part. The result will be a point on the number line that represents the mixed number.
Q: Can I use mixed numbers in geometry?
A: Yes, you can use mixed numbers in geometry to measure lengths and distances, calculate areas and volumes, and solve problems in trigonometry and calculus.