Evaluate The Expression: ${ 3 \frac{1}{5} \div 1 \frac{1}{3} = }$
Introduction
In mathematics, division is a fundamental operation that involves finding the quotient of two numbers. When dealing with mixed numbers, which are a combination of a whole number and a fraction, division can be a bit more complex. In this article, we will evaluate the expression 3 1/5 ÷ 1 1/3 and explore the steps involved in solving it.
Understanding Mixed Numbers
Before we dive into the evaluation of the expression, let's take a closer look at mixed numbers. A mixed number is a combination of a whole number and a fraction. It is typically written in the form a b/c, where a is the whole number and b/c is the fraction. For example, 3 1/5 is a mixed number that consists of a whole number 3 and a fraction 1/5.
Evaluating the Expression
To evaluate the expression 3 1/5 ÷ 1 1/3, we need to follow the order of operations (PEMDAS). The first step is to convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.
- 3 1/5 = (3 × 5) + 1 = 16/5
- 1 1/3 = (1 × 3) + 1 = 4/3
Evaluating the Division
Now that we have converted the mixed numbers to improper fractions, we can evaluate the division. To divide two fractions, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply the two fractions.
- 16/5 ÷ 4/3 = (16/5) × (3/4)
Multiplying the Fractions
To multiply two fractions, we need to multiply the numerators and denominators separately.
- (16/5) × (3/4) = (16 × 3) / (5 × 4)
- = 48/20
Simplifying the Result
The result of the division is 48/20. However, this fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
- GCD(48, 20) = 4
- 48 ÷ 4 = 12
- 20 ÷ 4 = 5
- 48/20 = 12/5
Conclusion
In conclusion, the expression 3 1/5 ÷ 1 1/3 can be evaluated by converting the mixed numbers to improper fractions and then dividing the fractions. The result of the division is 12/5, which can be simplified to 2 2/5.
Frequently Asked Questions
- Q: What is the result of 3 1/5 ÷ 1 1/3?
- A: The result of 3 1/5 ÷ 1 1/3 is 12/5, which can be simplified to 2 2/5.
- 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 then add the numerator. The result is then written as the new numerator over the denominator.
- Q: How do I divide two fractions?
- A: To divide two fractions, invert the second fraction (i.e., flip the numerator and denominator) and then multiply the two fractions.
Final Thoughts
In this article, we evaluated the expression 3 1/5 ÷ 1 1/3 and explored the steps involved in solving it. We learned how to convert mixed numbers to improper fractions and how to divide fractions. By following the order of operations and using the correct techniques, we can solve complex mathematical expressions with ease.
Introduction
In our previous article, we evaluated the expression 3 1/5 ÷ 1 1/3 and explored the steps involved in solving it. We learned how to convert mixed numbers to improper fractions and how to divide fractions. In this article, we will answer some frequently asked questions related to evaluating expressions with mixed numbers.
Q&A
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, while an improper fraction is a fraction where the numerator is greater than or equal to 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 then add the numerator. The result is then written as the new numerator over the denominator.
Q: How do I divide two fractions?
A: To divide two fractions, invert the second fraction (i.e., flip the numerator and denominator) and then multiply the two fractions.
Q: What is the order of operations when evaluating expressions with mixed numbers?
A: The order of operations is:
- Convert mixed numbers to improper fractions
- Invert the second fraction (if dividing)
- Multiply the fractions
- Simplify the result
Q: Can I simplify a fraction before dividing?
A: Yes, you can simplify a fraction before dividing. However, make sure to simplify the fraction after the division, not before.
Q: How do I add or subtract fractions with different denominators?
A: To add or subtract fractions with different denominators, find the least common multiple (LCM) of the denominators and then convert each fraction to have the LCM as the denominator.
Q: What is the least common multiple (LCM)?
A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.
Q: How do I find the LCM of two numbers?
A: To find the LCM of two numbers, list the multiples of each number and find the smallest number that appears in both lists.
Q: Can I use a calculator to evaluate expressions with mixed numbers?
A: Yes, you can use a calculator to evaluate expressions with mixed numbers. However, make sure to check your work and understand the steps involved in solving the expression.
Conclusion
In conclusion, evaluating expressions with mixed numbers requires a clear understanding of fractions, mixed numbers, and the order of operations. By following the steps outlined in this article, you can confidently evaluate expressions with mixed numbers and simplify fractions.
Final Thoughts
Evaluating expressions with mixed numbers is an essential skill in mathematics. By mastering this skill, you can solve complex mathematical problems with ease and confidence. Remember to always follow the order of operations and simplify fractions carefully to ensure accurate results.
Additional Resources
- Mathway: A free online math problem solver that can help you evaluate expressions with mixed numbers.
- Khan Academy: A free online learning platform that offers video lessons and practice exercises on fractions and mixed numbers.
- Purplemath: A free online math resource that offers lessons and practice exercises on fractions, mixed numbers, and other math topics.
Frequently Asked Questions
- Q: What is the result of 2 3/4 ÷ 1 1/2?
- A: The result of 2 3/4 ÷ 1 1/2 is 11/6, which can be simplified to 1 5/6.
- Q: How do I convert 3 1/2 to an improper fraction?
- A: To convert 3 1/2 to an improper fraction, multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.
- Q: What is the least common multiple (LCM) of 6 and 8?
- A: The least common multiple (LCM) of 6 and 8 is 24.