Simplify The Expression: ${ 27 \frac{2}{3} \div \frac{1}{8} }$
Introduction
When dealing with fractions and mixed numbers, simplifying expressions can be a challenging task. However, with the right approach and techniques, it can be made easier. In this article, we will focus on simplifying the expression 27 2/3 ÷ 1/8. We will break down the problem step by step, using various mathematical concepts and techniques to arrive at the final solution.
Understanding the Problem
To simplify the expression 27 2/3 ÷ 1/8, we need to understand the concept of division with fractions. When we divide a fraction by another fraction, we can invert the second fraction and multiply instead. This is based on the rule that division is the same as multiplying by the reciprocal of the divisor.
Inverting the Second Fraction
To simplify the expression, we need to invert the second fraction, which is 1/8. The reciprocal of 1/8 is 8/1. So, we can rewrite the expression as:
27 2/3 ÷ 1/8 = 27 2/3 × 8/1
Multiplying the Fractions
Now that we have inverted the second fraction, we can multiply the two fractions together. To do this, we need to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately.
27 2/3 = 27 + 2/3 = 83/3
So, the expression becomes:
(83/3) × 8/1
Multiplying the Numerators and Denominators
To multiply the fractions, we need to multiply the numerators and denominators separately.
Numerators: 83 × 8 = 664 Denominators: 3 × 1 = 3
So, the expression becomes:
664/3
Simplifying the Result
The result, 664/3, is an improper fraction. To simplify it, we can divide the numerator by the denominator.
664 ÷ 3 = 221.33
So, the simplified result is 221 1/3.
Conclusion
In this article, we simplified the expression 27 2/3 ÷ 1/8 by inverting the second fraction and multiplying the two fractions together. We then multiplied the numerators and denominators separately and simplified the result to arrive at the final solution. This problem demonstrates the importance of understanding the concept of division with fractions and the rule of inverting the second fraction to simplify the expression.
Frequently Asked Questions
- Q: What is the rule for dividing fractions? A: The rule for dividing fractions is to invert the second fraction and multiply instead.
- Q: How do I simplify an expression with a mixed number and a fraction? A: To simplify an expression with a mixed number and a fraction, you need to convert the mixed number to an improper fraction and then follow the steps outlined in this article.
- Q: What is the final solution to the expression 27 2/3 ÷ 1/8? A: The final solution to the expression 27 2/3 ÷ 1/8 is 221 1/3.
Additional Resources
- For more information on simplifying expressions with fractions, visit the Khan Academy website.
- For a step-by-step guide on simplifying expressions with mixed numbers, visit the Mathway website.
- For a list of common fractions and their equivalents, visit the Fraction Calculator website.
Final Thoughts
Simplifying expressions with fractions and mixed numbers can be a challenging task, but with the right approach and techniques, it can be made easier. By understanding the concept of division with fractions and the rule of inverting the second fraction, you can simplify expressions like 27 2/3 ÷ 1/8 and arrive at the final solution.
Introduction
In our previous article, we simplified the expression 27 2/3 ÷ 1/8 by inverting the second fraction and multiplying the two fractions together. We then multiplied the numerators and denominators separately and simplified the result to arrive at the final solution. In this article, we will answer some frequently asked questions related to simplifying expressions with fractions and mixed numbers.
Q&A
Q: What is the rule for dividing fractions?
A: The rule for dividing fractions is to invert the second fraction and multiply instead. This means that if you have a fraction a/b divided by a fraction c/d, you can rewrite it as a/b × d/c.
Q: How do I simplify an expression with a mixed number and a fraction?
A: To simplify an expression with a mixed number and a fraction, you need to convert the mixed number to an improper fraction. To do this, multiply the whole number part by the denominator and add the numerator. Then, write the result as an improper fraction.
Q: What is the final solution to the expression 27 2/3 ÷ 1/8?
A: The final solution to the expression 27 2/3 ÷ 1/8 is 221 1/3.
Q: Can I simplify an expression with a negative fraction?
A: Yes, you can simplify an expression with a negative fraction. To do this, follow the same steps as before, but remember to keep the negative sign.
Q: How do I simplify an expression with a decimal fraction?
A: To simplify an expression with a decimal fraction, you can convert the decimal fraction to a fraction by writing it as a fraction with a denominator of 10 or 100. Then, follow the same steps as before.
Q: Can I simplify an expression with a variable fraction?
A: Yes, you can simplify an expression with a variable fraction. To do this, follow the same steps as before, but remember to keep the variable.
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, while a mixed number is a combination of a whole number and a 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 part by the denominator and add the numerator. Then, write the result as an improper fraction.
Q: Can I simplify an expression with a fraction and a percentage?
A: Yes, you can simplify an expression with a fraction and a percentage. To do this, convert the percentage to a fraction by dividing by 100. Then, follow the same steps as before.
Conclusion
In this article, we answered some frequently asked questions related to simplifying expressions with fractions and mixed numbers. We covered topics such as the rule for dividing fractions, simplifying expressions with mixed numbers, and converting fractions to decimals. We also discussed the difference between fractions and mixed numbers, and how to convert mixed numbers to improper fractions.
Additional Resources
- For more information on simplifying expressions with fractions, visit the Khan Academy website.
- For a step-by-step guide on simplifying expressions with mixed numbers, visit the Mathway website.
- For a list of common fractions and their equivalents, visit the Fraction Calculator website.
Final Thoughts
Simplifying expressions with fractions and mixed numbers can be a challenging task, but with the right approach and techniques, it can be made easier. By understanding the concept of division with fractions and the rule of inverting the second fraction, you can simplify expressions like 27 2/3 ÷ 1/8 and arrive at the final solution.