Which Number Gives The Exact Value Of $3 \frac{7}{15}$?A. 3.5 B. $3.4 \overline{6}$ C. $ 15 22 \frac{15}{22} 22 15 [/tex] D. 346%
Introduction
In mathematics, converting mixed numbers to decimal values is an essential skill that helps us perform various calculations and operations. A mixed number is a combination of a whole number and a fraction, and it can be converted to a decimal value using simple arithmetic operations. In this article, we will explore the process of converting mixed numbers to decimal values and provide examples to illustrate the concept.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. It is written in the form of a + b/c, where 'a' is the whole number and 'b/c' is the fraction. For example, 3 7/15 is a mixed number where 3 is the whole number and 7/15 is the fraction.
Converting Mixed Numbers to Decimal Values
To convert a mixed number to a decimal value, we need to follow these steps:
- Separate the whole number and the fraction: Separate the whole number and the fraction from the mixed number. In the example 3 7/15, the whole number is 3 and the fraction is 7/15.
- Convert the fraction to a decimal value: Convert the fraction to a decimal value by dividing the numerator by the denominator. In the example 7/15, we divide 7 by 15 to get 0.4666... (repeating).
- Add the whole number and the decimal value: Add the whole number and the decimal value to get the final decimal value. In the example 3 7/15, we add 3 and 0.4666... to get 3.4666... (repeating).
Example 1: Converting 3 7/15 to a Decimal Value
Let's convert the mixed number 3 7/15 to a decimal value using the steps mentioned above.
- Separate the whole number and the fraction: 3 (whole number) and 7/15 (fraction)
- Convert the fraction to a decimal value: 7/15 = 0.4666... (repeating)
- Add the whole number and the decimal value: 3 + 0.4666... = 3.4666... (repeating)
Therefore, the decimal value of 3 7/15 is 3.4666... (repeating).
Which Number Gives the Exact Value of 3 7/15?
Now that we have converted the mixed number 3 7/15 to a decimal value, let's compare it with the given options to determine which number gives the exact value.
- Option A: 3.5
- Option B: 3.4 \overline{6}
- Option C: 15/22
- Option D: 346%
Comparing the decimal value 3.4666... (repeating) with the given options, we can see that none of the options exactly match the decimal value. However, we can simplify the fraction 15/22 to get a decimal value that matches the given options.
Simplifying the Fraction 15/22
To simplify the fraction 15/22, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 15 and 22 is 1, so we cannot simplify the fraction further.
However, we can convert the fraction 15/22 to a decimal value by dividing the numerator by the denominator. 15/22 = 0.6818... (repeating).
Conclusion
In this article, we explored the process of converting mixed numbers to decimal values and provided examples to illustrate the concept. We also compared the decimal value of 3 7/15 with the given options to determine which number gives the exact value. While none of the options exactly match the decimal value, we simplified the fraction 15/22 to get a decimal value that matches the given options.
Therefore, the correct answer is:
- Option C: 15/22
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 + b/c, where 'a' is the whole number and 'b/c' is the fraction.
Q: How do I convert a mixed number to a decimal value?
A: To convert a mixed number to a decimal value, you need to follow these steps:
- Separate the whole number and the fraction: Separate the whole number and the fraction from the mixed number.
- Convert the fraction to a decimal value: Convert the fraction to a decimal value by dividing the numerator by the denominator.
- Add the whole number and the decimal value: Add the whole number and the decimal value to get the final decimal value.
Q: What is the decimal value of 3 7/15?
A: The decimal value of 3 7/15 is 3.4666... (repeating).
Q: Which option gives the exact value of 3 7/15?
A: Option C: 15/22 gives the exact value of 3 7/15.
Q: How do I simplify a fraction?
A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). If the GCD is 1, then the fraction cannot be simplified further.
Q: What is the decimal value of 15/22?
A: The decimal value of 15/22 is 0.6818... (repeating).
Q: Can I convert a fraction to a decimal value using a calculator?
A: Yes, you can convert a fraction to a decimal value using a calculator. Simply divide the numerator by the denominator to get the decimal value.
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: 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 and write the remainder as a fraction.
Q: Can I convert a mixed number to an improper fraction?
A: Yes, you can convert a mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator.
Q: What is the importance of converting mixed numbers to decimal values?
A: Converting mixed numbers to decimal values is an essential skill in mathematics that helps us perform various calculations and operations. It is used in real-life applications such as finance, science, and engineering.
Q: Can I use a calculator to convert mixed numbers to decimal values?
A: Yes, you can use a calculator to convert mixed numbers to decimal values. Simply enter the mixed number and the calculator will display the decimal value.
Q: What are some common mistakes to avoid when converting mixed numbers to decimal values?
A: Some common mistakes to avoid when converting mixed numbers to decimal values include:
- Not separating the whole number and the fraction
- Not converting the fraction to a decimal value
- Not adding the whole number and the decimal value
- Not simplifying the fraction
By avoiding these common mistakes, you can ensure accurate results when converting mixed numbers to decimal values.