Express 31% as a fraction in its lowest form
The Correct Answer and Explanation is :
To express 31% as a fraction in its lowest form, follow these steps:
- Understanding Percentages: The term “percent” means “per hundred.” Therefore, 31% can be interpreted as (31) out of (100), which can be written as the fraction:
[
\frac{31}{100}
] - Reducing the Fraction: To simplify this fraction, we need to check if there are any common factors between the numerator (31) and the denominator (100).
- The number (31) is a prime number, meaning it has no positive divisors other than (1) and (31) itself.
- The number (100) can be factored into its prime components: (100 = 2^2 \times 5^2). Its divisors include (1, 2, 4, 5, 10, 20, 25, 50,) and (100).
- Finding Common Factors: Since (31) is a prime number and does not divide (100) evenly, the only common factor between (31) and (100) is (1). Therefore, the greatest common divisor (GCD) is (1).
- Conclusion: Since the GCD is (1), the fraction (\frac{31}{100}) is already in its simplest form.
Thus, (31\%) expressed as a fraction in its lowest terms is:
[
\frac{31}{100}
]
Summary
In summary, converting a percentage to a fraction involves understanding its definition, finding the corresponding numerator and denominator, and simplifying the fraction by identifying any common factors. For (31\%), this results in (\frac{31}{100}), which cannot be simplified further due to the prime nature of (31) and the lack of common factors with (100). This method of conversion is applicable to any percentage and is fundamental in mathematics for tasks involving ratios and comparisons.