How do you write 250% as a fraction, mixed number, or whole number in simplest form?
The Correct Answer and Explanation is :
To express 250% as a fraction, mixed number, or whole number in simplest form, we can follow a systematic approach.
Converting Percent to Fraction
- Understanding Percent: The term “percent” means “per hundred.” Therefore, 250% can be expressed as a fraction:
[
250\% = \frac{250}{100}
] - Simplifying the Fraction: Next, we simplify the fraction (\frac{250}{100}). To do this, we need to find the greatest common divisor (GCD) of the numerator and denominator.
- The GCD of 250 and 100 is 50.
- We divide both the numerator and the denominator by their GCD:
[
\frac{250 \div 50}{100 \div 50} = \frac{5}{2}
]
Mixed Number Form
To convert the improper fraction (\frac{5}{2}) into a mixed number, we divide the numerator by the denominator:
- Performing the Division:
- (5 \div 2 = 2) with a remainder of 1.
- Writing as a Mixed Number:
- The whole number part is 2, and the remainder (1) becomes the numerator of the fractional part, with 2 as the denominator. Thus, (\frac{5}{2}) can be written as:
[
2 \frac{1}{2}
]
Whole Number Form
Since 250% is greater than 100%, it cannot be expressed as a whole number. However, we can consider the whole number part of our mixed number. The whole number part is 2.
Summary
In conclusion, 250% can be expressed as:
- Fraction: (\frac{5}{2})
- Mixed Number: (2 \frac{1}{2})
- Whole Number: 2 (noting that it represents only the whole number part of the mixed number).
Understanding how to convert percentages to other forms enhances mathematical literacy and helps in various real-world applications, such as finance and statistics, where percentages are commonly used.