Write The Mixed Number { 13 \frac{39}{49} $}$ As An Improper Fraction.
Understanding Mixed Numbers and Improper Fractions
In mathematics, a mixed number is a combination of a whole number and a proper fraction. It is written in the form of a whole number followed by a fraction. For example, 13 \frac{39}{49} is a mixed number where 13 is the whole number and \frac{39}{49} is the proper fraction. On the other hand, an improper fraction is a fraction where the numerator is greater than the denominator. For instance, \frac{39}{49} is a proper fraction, but if the numerator is greater than the denominator, it becomes an improper fraction.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we need to follow a simple step-by-step process. The process involves multiplying the whole number by the denominator and then adding the numerator to the product. The result is then written as the new numerator over the denominator.
Step 1: Multiply the Whole Number by the Denominator
In the given mixed number 13 \frac{39}{49}, we need to multiply the whole number 13 by the denominator 49.
13 × 49 = 637
Step 2: Add the Numerator to the Product
Now, we add the numerator 39 to the product 637.
637 + 39 = 676
Step 3: Write the Result as the New Numerator Over the Denominator
The result 676 is the new numerator, and the denominator remains the same, which is 49.
Therefore, the mixed number 13 \frac{39}{49} can be written as an improper fraction as follows:
\frac{676}{49}
Example of Converting Mixed Numbers to Improper Fractions
Let's consider another example to understand the process better. Suppose we have a mixed number 25 \frac{17}{24}. To convert it to an improper fraction, we follow the same steps.
Step 1: Multiply the Whole Number by the Denominator
25 × 24 = 600
Step 2: Add the Numerator to the Product
600 + 17 = 617
Step 3: Write the Result as the New Numerator Over the Denominator
The result 617 is the new numerator, and the denominator remains the same, which is 24.
Therefore, the mixed number 25 \frac{17}{24} can be written as an improper fraction as follows:
\frac{617}{24}
Benefits of Converting Mixed Numbers to Improper Fractions
Converting mixed numbers to improper fractions has several benefits. It makes the calculations easier and more efficient. For instance, when we have a mixed number in a mathematical expression, it can be challenging to perform operations like addition and subtraction. However, when we convert it to an improper fraction, the calculations become simpler.
Moreover, improper fractions are more convenient when we need to perform operations like multiplication and division. For example, when we multiply two mixed numbers, it can be a tedious process. However, when we convert them to improper fractions, the multiplication becomes straightforward.
Conclusion
In conclusion, converting mixed numbers to improper fractions is a simple process that involves multiplying the whole number by the denominator and adding the numerator to the product. The result is then written as the new numerator over the denominator. This process has several benefits, including making calculations easier and more efficient. By converting mixed numbers to improper fractions, we can simplify mathematical expressions and perform operations more conveniently.
Frequently Asked Questions
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 of a whole number followed by a fraction.
Q: What is an improper fraction?
A: An improper fraction is a fraction where the numerator is greater than the denominator.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator to the product. The result is then written as the new numerator over the denominator.
Q: Why is it beneficial to convert mixed numbers to improper fractions?
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 of a whole number followed by a fraction. For example, 13 \frac{39}{49} is a mixed number where 13 is the whole number and \frac{39}{49} is the proper fraction.
Q: What is an improper fraction?
A: An improper fraction is a fraction where the numerator is greater than the denominator. For instance, \frac{39}{49} is a proper fraction, but if the numerator is greater than the denominator, it becomes an improper fraction.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator to the product. The result is then written as the new numerator over the denominator. For example, to convert 13 \frac{39}{49} to an improper fraction, we multiply 13 by 49 and add 39 to the product.
13 × 49 = 637 637 + 39 = 676
Therefore, the mixed number 13 \frac{39}{49} can be written as an improper fraction as follows:
\frac{676}{49}
Q: Why is it beneficial to convert mixed numbers to improper fractions?
A: Converting mixed numbers to improper fractions makes calculations easier and more efficient. It also simplifies mathematical expressions and makes operations like multiplication and division more straightforward.
Q: Can I convert a mixed number to an improper fraction by using a calculator?
A: Yes, you can convert a mixed number to an improper fraction by using a calculator. Simply multiply the whole number by the denominator and add the numerator to the product. The result will be the new numerator over the denominator.
Q: How do I add or subtract mixed numbers?
A: To add or subtract mixed numbers, you need to convert them to improper fractions first. Then, you can add or subtract the numerators and keep the denominator the same. Finally, simplify the result to get the final answer.
Q: Can I multiply or divide mixed numbers?
A: Yes, you can multiply or divide mixed numbers, but it's easier to convert them to improper fractions first. Then, you can multiply or divide the numerators and keep the denominators the same. Finally, simplify the result to get the final answer.
Q: What is the difference between a mixed number and an improper fraction?
A: The main difference between a mixed number and an improper fraction is the way they are written. A mixed number is written as a whole number followed by a fraction, while an improper fraction is written as a fraction where the numerator is greater than the denominator.
Q: Can I convert an improper fraction to a mixed number?
A: Yes, you can convert an improper fraction to a mixed number by dividing the numerator by the denominator and writing the result as a whole number followed by a 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 and write the result as a whole number followed by a fraction. For example, to convert \frac{676}{49} to a mixed number, we divide 676 by 49.
676 ÷ 49 = 13 with a remainder of 39
Therefore, the improper fraction \frac{676}{49} can be written as a mixed number as follows:
13 \frac{39}{49}
Q: What are some real-life applications of mixed numbers and improper fractions?
A: Mixed numbers and improper fractions have many real-life applications in fields such as finance, engineering, and science. For example, in finance, mixed numbers and improper fractions are used to calculate interest rates and investment returns. In engineering, they are used to calculate distances and measurements. In science, they are used to calculate quantities and measurements.
Q: Can I use a calculator to convert mixed numbers to improper fractions?
A: Yes, you can use a calculator to convert mixed numbers to improper fractions. Simply enter the mixed number and the calculator will convert it to an improper fraction for you.
Q: How do I simplify a mixed number or an improper fraction?
A: To simplify a mixed number or an improper fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both the numerator and the denominator by the GCD to simplify the fraction.
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction 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 find the GCD of two numbers?
A: To find the GCD of two numbers, you can use the Euclidean algorithm or list the factors of each number and find the greatest common factor. For example, to find the GCD of 12 and 18, we can list the factors of each number and find the greatest common factor.
Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18
The greatest common factor of 12 and 18 is 6.
Q: Can I use a calculator to find the GCD of two numbers?
A: Yes, you can use a calculator to find the GCD of two numbers. Simply enter the two numbers and the calculator will find the GCD for you.
Q: What are some common mistakes to avoid when working with mixed numbers and improper fractions?
A: Some common mistakes to avoid when working with mixed numbers and improper fractions include:
- Not converting mixed numbers to improper fractions before performing operations
- Not simplifying fractions before performing operations
- Not using the correct order of operations when performing calculations
- Not checking for errors when converting mixed numbers to improper fractions
By avoiding these common mistakes, you can ensure that your calculations are accurate and reliable.