Write 8 1/3 as a proper fraction
The Correct Answer and Explanation is :
To convert the mixed number (8 \frac{1}{3}) into a proper fraction, follow these steps:
- Identify the whole number and the fraction: In (8 \frac{1}{3}), the whole number is 8, and the fraction is (\frac{1}{3}).
- Convert the whole number to a fraction: To convert the whole number (8) into a fraction, multiply it by the denominator of the fractional part (which is 3). This can be expressed as:
[
8 = \frac{8 \times 3}{3} = \frac{24}{3}
] - Add the fraction: Now, add the fractional part (\frac{1}{3}) to the converted whole number:
[
\frac{24}{3} + \frac{1}{3} = \frac{24 + 1}{3} = \frac{25}{3}
]
Thus, the mixed number (8 \frac{1}{3}) can be expressed as the improper fraction (\frac{25}{3}).
Explanation:
A mixed number consists of both a whole number and a proper fraction. Converting it to an improper fraction is useful, especially in mathematical operations such as addition, subtraction, multiplication, and division, where improper fractions are often easier to work with.
In our example, (8 \frac{1}{3}) indicates that there are 8 whole parts, each equivalent to a unit of 3 (the denominator). To find the equivalent improper fraction, we convert the whole part into a fraction with the same denominator as the fractional part.
The process helps to maintain the value of the mixed number while enabling more straightforward calculations. The resulting improper fraction (\frac{25}{3}) can also be used in various mathematical operations, such as comparing with other fractions or converting back into a mixed number if needed. Understanding how to convert between mixed numbers and improper fractions is fundamental in fraction operations and enhances overall mathematical proficiency.
In summary, (8 \frac{1}{3}) is equivalent to (\frac{25}{3}) as an improper fraction, demonstrating a common and essential conversion in fraction arithmetic.