What is 3/20 as a simplified fraction?
The Correct Answer and Explanation is:
The fraction ( \frac{3}{20} ) is already in its simplest form. To understand why this fraction is simplified, it’s important to review some basic concepts about fractions and simplification.
Definition of a Fraction:
A fraction consists of two numbers: the numerator (the top number) and the denominator (the bottom number). In the case of ( \frac{3}{20} ), the numerator is 3, and the denominator is 20. The fraction represents the division of the numerator by the denominator, or in other words, it tells us how many parts of a whole are being considered.
Simplifying a Fraction:
A fraction is said to be in simplest form when the numerator and denominator have no common factors other than 1. This means that they cannot be divided by the same number evenly, aside from 1. To simplify a fraction, one must find the greatest common divisor (GCD) of the numerator and denominator and then divide both by that number.
Finding the GCD:
In this case, we need to find the GCD of 3 and 20. The factors of 3 are 1 and 3, while the factors of 20 are 1, 2, 4, 5, 10, and 20. The only common factor between 3 and 20 is 1. Since the GCD is 1, we cannot divide the numerator and denominator by any other number to simplify the fraction further.
Conclusion:
Therefore, ( \frac{3}{20} ) is already in its simplest form. It is a proper fraction, meaning that the numerator is less than the denominator, indicating that it represents a value less than 1. In practical applications, this fraction might be encountered in various scenarios, such as in cooking measurements, statistics, or probability calculations. Understanding how to simplify fractions is essential for performing arithmetic operations, comparing fractions, and applying them in real-world situations.