Convert 2
5
1
to an improper fraction.
The Correct Answer and Explanation is :
To convert the mixed number (2 \frac{5}{1}) into an improper fraction, we follow a systematic process. A mixed number consists of a whole number and a proper fraction. In this case, the whole number is 2, and the fraction is ( \frac{5}{1} ), which is equivalent to 5 as it has 5 as the numerator and 1 as the denominator.
Step-by-Step Conversion
- Multiply the Whole Number by the Denominator:
In this mixed number, the whole number is 2, and the denominator of the fraction is 1. We multiply these together:
[
2 \times 1 = 2
] - Add the Numerator of the Fraction:
Next, we add the result from the first step to the numerator of the fraction (which is 5):
[
2 + 5 = 7
] - Place the Result Over the Original Denominator:
Finally, we take the result from step 2 (which is 7) and place it over the original denominator (1):
[
\frac{7}{1}
]
Thus, the improper fraction for the mixed number (2 \frac{5}{1}) is (\frac{7}{1}).
Understanding Improper Fractions
An improper fraction is defined as a fraction where the numerator is greater than or equal to the denominator. In our case, (\frac{7}{1}) is indeed an improper fraction because the numerator (7) is greater than the denominator (1).
Additionally, it’s important to note that improper fractions can easily be converted back to mixed numbers. For example, dividing the numerator (7) by the denominator (1) results in a quotient of 7, which is a whole number, indicating that there are no fractional parts remaining.
In mathematical operations, improper fractions are often easier to work with, especially in addition and subtraction involving fractions, as they allow for a straightforward comparison of sizes and values.
In summary, the mixed number (2 \frac{5}{1}) converts to the improper fraction (\frac{7}{1}), demonstrating the process of multiplying the whole number by the denominator, adding the numerator, and placing it over the denominator.