What is the simplest form of 3/100?
The Correct Answer and Explanation is:
The simplest form of the fraction ( \frac{3}{100} ) is ( \frac{3}{100} ) itself. This is because the numerator (3) and the denominator (100) do not have any common factors other than 1.
Understanding Simplification
To simplify a fraction, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
- Identifying Factors:
- The factors of 3 are 1 and 3.
- The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
- Finding the GCD:
- The only common factor between 3 and 100 is 1. Therefore, the GCD is 1.
- Dividing by the GCD:
- To simplify ( \frac{3}{100} ), we divide both the numerator and denominator by their GCD:
[
\frac{3 \div 1}{100 \div 1} = \frac{3}{100}
]
Since the GCD is 1, we see that ( \frac{3}{100} ) is already in its simplest form.
Conclusion
In practical terms, simplifying fractions is crucial in various fields, such as mathematics, cooking, and finance, where clear and concise representation of quantities is important. Keeping a fraction in its simplest form makes it easier to compare, add, or subtract with other fractions.
For example, if you were to add ( \frac{3}{100} ) to ( \frac{2}{100} ), it would be straightforward because both fractions share the same denominator. Thus, the importance of simplification lies not only in clarity but also in enhancing mathematical operations.
In summary, ( \frac{3}{100} ) cannot be simplified further, as it is already in its simplest form.