What Is \[$1 \frac{2}{3}\$\] As An Improper Fraction?A) \[$\frac{2}{3}\$\] B) \[$\frac{8}{3}\$\] C) \[$\frac{6}{3}\$\] D) \[$\frac{5}{3}\$\]
What is ${1 \frac{2}{3}\$} 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 represented as the sum of a whole number and a fraction. For example, ${1 \frac{2}{3}\$} is a mixed number where 1 is the whole number and {\frac{2}{3}$}$ is the proper fraction. On the other hand, an improper fraction is a fraction where the numerator is greater than or equal to the denominator. It is represented as a single fraction without any whole number part.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we need to multiply the whole number part by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same. Let's apply this rule to the mixed number ${1 \frac{2}{3}\$}.
Step 1: Multiply the Whole Number by the Denominator
In the mixed number ${1 \frac{2}{3}\$}, the whole number is 1 and the denominator is 3. We multiply 1 by 3 to get 3.
Step 2: Add the Numerator
Now, we add the numerator (2) to the result of the multiplication (3) to get the new numerator. The new numerator is 5.
Step 3: Write the Improper Fraction
The denominator remains the same, which is 3. Therefore, the improper fraction equivalent of the mixed number ${1 \frac{2}{3}\$} is {\frac{5}{3}$}$.
Conclusion
In conclusion, the improper fraction equivalent of the mixed number ${1 \frac{2}{3}\$} is {\frac{5}{3}$}$. This is the correct answer among the options provided.
Answer
The correct answer is D) {\frac{5}{3}$}$.
Why is this the Correct Answer?
This is the correct answer because we have followed the correct steps to convert the mixed number to an improper fraction. We have multiplied the whole number by the denominator, added the numerator, and written the improper fraction with the new numerator and the same denominator.
What is the Importance of Converting Mixed Numbers to Improper Fractions?
Converting mixed numbers to improper fractions is an essential skill in mathematics. It helps us to perform arithmetic operations, such as addition and subtraction, with fractions. It also helps us to compare fractions and to solve problems involving fractions.
How to Convert Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we need to follow the steps outlined above. We multiply the whole number by the denominator, add the numerator, and write the improper fraction with the new numerator and the same denominator.
Common Mistakes to Avoid
When converting mixed numbers to improper fractions, we need to avoid common mistakes. One common mistake is to forget to multiply the whole number by the denominator. Another common mistake is to add the numerator to the denominator instead of multiplying the whole number by the denominator.
Real-World Applications
Converting mixed numbers to improper fractions has real-world applications. For example, in cooking, we may need to convert a mixed number of cups to an improper fraction to measure the ingredients accurately. In construction, we may need to convert a mixed number of feet to an improper fraction to measure the length of a room accurately.
Conclusion
In conclusion, converting mixed numbers to improper fractions is an essential skill in mathematics. It helps us to perform arithmetic operations, such as addition and subtraction, with fractions. It also helps us to compare fractions and to solve problems involving fractions. By following the correct steps and avoiding common mistakes, we can convert mixed numbers to improper fractions accurately and confidently.
Final Answer
The final answer is D) {\frac{5}{3}$}$.
Q&A: Converting Mixed Numbers to Improper Fractions
Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions about converting 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 represented as the sum of a whole number and a fraction.
Q: What is an improper fraction?
A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. It is represented as a single fraction without any whole number part.
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 by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same.
Q: What is the formula for converting a mixed number to an improper fraction?
A: The formula for converting a mixed number to an improper fraction is:
New Numerator = (Whole Number x Denominator) + Numerator
Q: How do I write the improper fraction?
A: The improper fraction is written with the new numerator and the same denominator. For example, if the mixed number is ${1 \frac{2}{3}\$}, the improper fraction is {\frac{5}{3}$}$.
Q: What are some common mistakes to avoid when converting mixed numbers to improper fractions?
A: Some common mistakes to avoid when converting mixed numbers to improper fractions include:
- Forgetting to multiply the whole number by the denominator
- Adding the numerator to the denominator instead of multiplying the whole number by the denominator
- Writing the improper fraction with the wrong numerator or denominator
Q: Why is it important to convert mixed numbers to improper fractions?
A: Converting mixed numbers to improper fractions is important because it helps us to perform arithmetic operations, such as addition and subtraction, with fractions. It also helps us to compare fractions and to solve problems involving fractions.
Q: How do I apply this skill in real-world situations?
A: You can apply this skill in real-world situations such as:
- Cooking: Converting mixed numbers of cups to improper fractions to measure ingredients accurately
- Construction: Converting mixed numbers of feet to improper fractions to measure the length of a room accurately
- Science: Converting mixed numbers of grams to improper fractions to measure the weight of a substance accurately
Q: What are some examples of mixed numbers that can be converted to improper fractions?
A: Some examples of mixed numbers that can be converted to improper fractions include:
- ${2 \frac{1}{4}\$\) = \[\frac{9}{4}$}$
- ${3 \frac{2}{5}\$\) = \[\frac{17}{5}$}$
- ${4 \frac{3}{8}\$\) = \[\frac{35}{8}$}$
Conclusion
In conclusion, converting mixed numbers to improper fractions is an essential skill in mathematics. It helps us to perform arithmetic operations, such as addition and subtraction, with fractions. It also helps us to compare fractions and to solve problems involving fractions. By following the correct steps and avoiding common mistakes, we can convert mixed numbers to improper fractions accurately and confidently.
Final Answer
The final answer is D) {\frac{5}{3}$}$.