What Is $\frac{7}{4}$ As A Mixed Number?A) $\frac{3}{4}$ B) \$\frac{13}{4}$[/tex\] C) $\frac{1}{4}$ D) $\frac{17}{4}$
What is $\frac{7}{4}$ as a Mixed Number?
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, where the fraction is in its simplest form. For example, 3$\frac{1}{4}$ is a mixed number, where 3 is the whole number and $\frac{1}{4}$ is the fraction.
Converting an Improper Fraction to a Mixed Number
To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. The quotient will be the whole number, and the remainder will be the new numerator. The denominator remains the same.
Step-by-Step Solution
To convert $\frac{7}{4}$ to a mixed number, we will follow these steps:
- Divide the numerator (7) by the denominator (4).
- The quotient will be the whole number.
- The remainder will be the new numerator.
- The denominator remains the same.
Performing the Division
7 ÷ 4 = 1 with a remainder of 3.
Writing the Mixed Number
The whole number is 1, and the remainder (3) becomes the new numerator. The denominator remains the same (4). Therefore, $\frac{7}{4}$ as a mixed number is 1$\frac{3}{4}$.
Evaluating the Answer Choices
Now that we have found the mixed number equivalent of $\frac{7}{4}$, let's evaluate the answer choices:
A) $\frac{3}{4}$ - This is not the correct answer, as it is a fraction and not a mixed number.
B) $\frac{13}{4}$ - This is not the correct answer, as it is an improper fraction and not a mixed number.
C) $\frac{1}{4}$ - This is not the correct answer, as it is a fraction and not a mixed number.
D) $\frac{17}{4}$ - This is not the correct answer, as it is an improper fraction and not a mixed number.
Conclusion
The correct answer is not among the options provided. However, we have found that $\frac{7}{4}$ as a mixed number is 1$\frac{3}{4}$. This is not an option, but it is the correct answer.
Why is this Important?
Understanding how to convert improper fractions to mixed numbers is an important skill in mathematics. It is used in a variety of applications, such as cooking, building, and finance. Being able to convert between improper fractions and mixed numbers can help you to better understand and work with fractions in general.
Real-World Applications
Mixed numbers are used in a variety of real-world applications, such as:
- Cooking: When a recipe calls for a certain amount of an ingredient, it may be written as a mixed number. For example, a recipe may call for 2$\frac{1}{4}$ cups of flour.
- Building: When building a structure, measurements may be written as mixed numbers. For example, a wall may be 3$\frac{1}{2}$ feet high.
- Finance: When working with money, mixed numbers may be used to represent amounts. For example, a bank account may have a balance of 1$\frac{3}{4}$ dollars.
Conclusion
In conclusion, $\frac{7}{4}$ as a mixed number is 1$\frac{3}{4}$. This is an important skill to understand, as it is used in a variety of real-world applications. Being able to convert between improper fractions and mixed numbers can help you to better understand and work with fractions in general.
Frequently Asked Questions: Mixed Numbers
Q: What is a mixed number?
A: A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, where the fraction is in its simplest form.
Q: How do I convert an improper fraction to a mixed number?
A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator. The quotient will be the whole number, and the remainder will be the new numerator. The denominator remains the same.
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 the denominator.
Q: Can I simplify a mixed number?
A: Yes, you can simplify a mixed number by simplifying the fraction part. For example, 2$\frac{1}{2}$ can be simplified to 2$\frac{1}{2}$, but 2$\frac{3}{6}$ can be simplified to 2$\frac{1}{2}$.
Q: How do I add or subtract mixed numbers?
A: To add or subtract mixed numbers, you need to add or subtract the whole numbers and then add or subtract the fractions. For example, 2$\frac{1}{2}$ + 3$\frac{1}{4}$ = 5$\frac{3}{4}$.
Q: Can I multiply or divide mixed numbers?
A: Yes, you can multiply or divide mixed numbers, but you need to convert them to improper fractions first. For example, 2$\frac{1}{2}$ × 3$\frac{1}{4}$ = $\frac{5}{2}$ × $\frac{13}{4}$ = $\frac{65}{8}$.
Q: What are some real-world applications of mixed numbers?
A: Mixed numbers are used in a variety of real-world applications, such as cooking, building, and finance. For example, a recipe may call for 2$\frac{1}{4}$ cups of flour, or a wall may be 3$\frac{1}{2}$ feet high.
Q: Can I use a calculator to convert an improper fraction to a mixed number?
A: Yes, you can use a calculator to convert an improper fraction to a mixed number. However, it's always a good idea to understand the concept and be able to do it manually.
Q: What are some common mistakes to avoid when working with mixed numbers?
A: Some common mistakes to avoid when working with mixed numbers include:
- Forgetting to simplify the fraction part
- Adding or subtracting the whole numbers and fractions separately
- Not converting mixed numbers to improper fractions when multiplying or dividing
- Not simplifying the fraction part when adding or subtracting mixed numbers
Conclusion
Mixed numbers are an important concept in mathematics, and understanding how to work with them can help you to better understand and work with fractions in general. By following the steps outlined in this article and practicing with examples, you can become more confident and proficient in working with mixed numbers.