Rewriting the Mixed Number as a Fraction

Oct 13, 2025 by magicalceylontours.com 65 views

Introduction

In mathematics, solving for the unknown side of a problem often requires a combination of algebraic and arithmetic operations. One common scenario is when we are given a mixed number, such as $10 \frac{4}{5}$ , and asked to perform a division operation. In this article, we will explore how to rewrite the mixed number as a fraction greater than 1 and then perform the division operation.

Rewriting the Mixed Number as a Fraction

To rewrite the mixed number $10 \frac{4}{5}$ as a fraction greater than 1, we need to follow these steps:

Convert the mixed number to an improper fraction: To do this, we multiply the whole number part (10) by the denominator (5) and then add the numerator (4). This gives us: $10 \times 5 + 4 = 54$ .
Write the result as a fraction: The result from step 1 is the new numerator, and the denominator remains the same (5). So, we can write the mixed number as a fraction: $\frac{54}{5}$ .

Performing the Division Operation

Now that we have rewritten the mixed number as a fraction greater than 1, we can perform the division operation. The problem statement asks us to divide $\frac{54}{5}$ by 3. To do this, we can follow these steps:

Invert the divisor: To divide by a number, we can multiply by its reciprocal. In this case, the divisor is 3, so we can invert it by taking its reciprocal: $\frac{1}{3}$ .
Multiply the fraction by the reciprocal: Now that we have the reciprocal of the divisor, we can multiply the fraction by it: $\frac{54}{5} \times \frac{1}{3}$ .
Simplify the result: To simplify the result, we can multiply the numerators and denominators separately: $\frac{54 \times 1}{5 \times 3} = \frac{54}{15}$ .
Reduce the fraction: Finally, we can reduce the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 54 and 15 is 3, so we can divide both numbers by 3: $\frac{54 \div 3}{15 \div 3} = \frac{18}{5}$ .

Conclusion

In this article, we have shown how to rewrite a mixed number as a fraction greater than 1 and then perform a division operation. By following these steps, we can solve for the unknown side of a problem and arrive at the correct solution. Whether you are a student or a professional, mastering these skills will help you to tackle a wide range of mathematical problems with confidence.

Additional Tips and Tricks

Practice makes perfect: The more you practice rewriting mixed numbers as fractions and performing division operations, the more comfortable you will become with these skills.
Use a calculator: If you are struggling to simplify fractions or perform division operations, consider using a calculator to check your work.
Check your work: Always check your work to ensure that you have arrived at the correct solution.

Common Mistakes to Avoid

Forgetting to invert the divisor: When dividing by a number, make sure to invert it by taking its reciprocal.
Not simplifying the result: Make sure to simplify the result by multiplying the numerators and denominators separately.
Not reducing the fraction: Finally, make sure to reduce the fraction by dividing both the numerator and denominator by their GCD.

Real-World Applications

Cooking and recipes: When cooking, you may need to divide ingredients by a certain number. By mastering the skills we have discussed in this article, you can ensure that you have the correct amount of ingredients.
Shopping and discounts: When shopping, you may need to calculate discounts or percentages. By mastering the skills we have discussed in this article, you can ensure that you are getting the best deal.
Science and engineering: In science and engineering, you may need to perform complex calculations involving fractions and division. By mastering the skills we have discussed in this article, you can ensure that you are arriving at the correct solutions.

Conclusion

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

A: A mixed number is a combination of a whole number and a fraction, such as $10 \frac{4}{5}$ . An improper fraction, on the other hand, is a fraction where the numerator is greater than the denominator, such as $\frac{54}{5}$ .

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and then add the numerator. For example, to convert $10 \frac{4}{5}$ to an improper fraction, you would multiply 10 by 5 and add 4, resulting in $\frac{54}{5}$ .

Q: What is the reciprocal of a number?

A: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 3 is $\frac{1}{3}$ .

Q: How do I perform division with fractions?

A: To perform division with fractions, you need to invert the divisor (i.e., take its reciprocal) and then multiply the fraction by the reciprocal. For example, to divide $\frac{54}{5}$ by 3, you would invert the divisor (3) to get $\frac{1}{3}$ , and then multiply the fraction by the reciprocal: $\frac{54}{5} \times \frac{1}{3}$ .

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and denominator by their greatest common divisor (GCD). For example, to simplify $\frac{54}{15}$ , you would divide both numbers by 3, resulting in $\frac{18}{5}$ .

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 54 and 15 is 3.

Q: How do I reduce a fraction?

A: To reduce a fraction, you need to divide both the numerator and denominator by their GCD. For example, to reduce $\frac{54}{15}$ , you would divide both numbers by 3, resulting in $\frac{18}{5}$ .

Q: What are some common mistakes to avoid when working with fractions?

A: Some common mistakes to avoid when working with fractions include:

Forgetting to invert the divisor
Not simplifying the result
Not reducing the fraction
Not checking your work

Q: How can I practice solving for the unknown side?

A: You can practice solving for the unknown side by working through examples and exercises, such as:

Converting mixed numbers to improper fractions
Performing division with fractions
Simplifying fractions
Reducing fractions

Q: What are some real-world applications of solving for the unknown side?

A: Some real-world applications of solving for the unknown side include:

Cooking and recipes
Shopping and discounts
Science and engineering

Conclusion

In conclusion, solving for the unknown side of a problem often requires a combination of algebraic and arithmetic operations. By mastering the skills we have discussed in this article, you can ensure that you are arriving at the correct solutions. Whether you are a student or a professional, these skills will serve you well in a wide range of mathematical problems.