Write 75% as a simple fraction.
The correct answer and explanation is :
Correct Answer:
75% as a simple fraction is ¾.
Explanation (300 words):
To convert 75% into a simple fraction, follow these steps:
Step 1: Understand the Meaning of Percent
The term percent means “per hundred.” So, 75% can be written as:
[
75\% = \frac{75}{100}
]
This fraction represents 75 parts out of 100.
Step 2: Simplify the Fraction
To simplify (\frac{75}{100}), we find the greatest common divisor (GCD) of 75 and 100. The GCD is the largest number that divides both 75 and 100 without leaving a remainder.
- Prime Factorization:
- 75 = 3 × 5 × 5
- 100 = 2 × 2 × 5 × 5
The common factor is 5 × 5 = 25.
Now, divide both the numerator and denominator by 25:
[
\frac{75 \div 25}{100 \div 25} = \frac{3}{4}
]
Thus, 75% is equivalent to ¾ in its simplest form.
Step 3: Verify the Conversion
To check, convert ¾ back into a percentage:
[
\frac{3}{4} \times 100 = 75\%
]
This confirms our answer.
Step 4: Real-Life Applications
Fractions like ¾ appear in many real-world scenarios, such as:
- If you eat ¾ of a pizza, you have eaten 75% of it.
- If a store offers a 75% discount, you only pay ¼ of the original price.
Understanding fraction and percentage conversions is useful in mathematics, finance, cooking, and everyday decision-making.
Thus, 75% is ¾, a simplified and commonly used fraction.