What is 15/100 in simplest form
The Correct Answer and Explanation is :
The correct answer is: ( \frac{3}{20} )
To simplify the fraction ( \frac{15}{100} ), you need to find the greatest common divisor (GCD) of the numerator (15) and the denominator (100).
- Finding the GCD:
- The factors of 15 are: 1, 3, 5, 15.
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
- The largest factor that appears in both lists is 5, so the GCD of 15 and 100 is 5.
- Dividing by the GCD:
To simplify the fraction, divide both the numerator and the denominator by the GCD:
[
\frac{15 \div 5}{100 \div 5} = \frac{3}{20}
]
So, ( \frac{15}{100} ) simplifies to ( \frac{3}{20} ).
Explanation of Simplifying Fractions
Simplifying fractions means reducing them to their lowest terms, which makes them easier to understand and work with. The goal is to express the fraction in such a way that the numerator and denominator share no common factors other than 1.
To simplify a fraction, you typically start by identifying the GCD of the numerator and denominator. The GCD is the largest integer that divides both numbers without leaving a remainder. Once the GCD is found, you divide both the numerator and the denominator by this number.
In the case of ( \frac{15}{100} ):
- The process involved first determining the factors of both numbers to identify their GCD.
- After finding that the GCD is 5, dividing both 15 and 100 by 5 gives the simplified fraction ( \frac{3}{20} ).
This simplification is important in various applications, such as in cooking, measurements, and even in data analysis, where clear and concise representations are often required. By reducing fractions, we make calculations more manageable and improve clarity in communication.