How do you write 280% as a fraction or mixed numbers?
The correct answer and explanation is:
Correct Answer:
280% as a fraction is: 280100=145\frac{280}{100} = \frac{14}{5}
As a mixed number, this is: 2452\frac{4}{5}
300-Word Explanation:
To convert 280% into a fraction or mixed number, we first need to understand what percent means. The term “percent” comes from the Latin per centum, which means “per hundred.” So, 280% literally means 280 per 100, or: 280%=280100280\% = \frac{280}{100}
This is an improper fraction because the numerator (280) is greater than the denominator (100). To simplify this, we divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20: 280÷20100÷20=145\frac{280 \div 20}{100 \div 20} = \frac{14}{5}
So, the simplified fraction form of 280% is 14/5.
Now, to write this improper fraction as a mixed number, we divide 14 by 5:
- 5 goes into 14 two times (5 × 2 = 10),
- The remainder is 4.
So: 145=245\frac{14}{5} = 2\frac{4}{5}
Thus, 280% is equivalent to the mixed number 2 4/5.
This conversion is useful because sometimes it’s easier to understand or visualize values in fraction or mixed number form, especially when dealing with measurements, ratios, or real-life applications like recipes and distances. For example, saying “2 and 4/5 meters” may be more meaningful than saying “280% of a meter” in everyday situations. Additionally, expressing percentages as fractions helps in algebra, probability, and comparison problems.
So, the final answer is:
- As a fraction: 14/5
- As a mixed number: 2 4/5