What is the simplest form of 33/100
The Correct Answer and Explanation is:
The fraction ( \frac{33}{100} ) is already in its simplest form. To explain why, let’s break down the process of simplifying fractions.
Understanding Fractions
A fraction consists of two parts: the numerator (the top number) and the denominator (the bottom number). To simplify a fraction, we look for the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that can evenly divide both numbers.
Finding the GCD
- List the Factors:
- For ( 33 ), the factors are ( 1, 3, 11, 33 ).
- For ( 100 ), the factors are ( 1, 2, 4, 5, 10, 20, 25, 50, 100 ).
- Identify Common Factors:
The only common factor of ( 33 ) and ( 100 ) is ( 1 ). - Determine the GCD:
Since the only common factor is ( 1 ), the GCD of ( 33 ) and ( 100 ) is ( 1 ).
Simplifying the Fraction
To simplify a fraction, you divide both the numerator and denominator by their GCD:
[
\frac{33 \div 1}{100 \div 1} = \frac{33}{100}
]
Since the GCD is ( 1 ), dividing by ( 1 ) does not change the fraction. Therefore, ( \frac{33}{100} ) remains the same.
Conclusion
Since there are no common factors other than ( 1 ), ( \frac{33}{100} ) is already in its simplest form. This means that ( 33 ) and ( 100 ) cannot be simplified further without changing the value of the fraction. The fraction represents a value of ( 0.33 ) or ( 33\% ) when converted to decimal or percentage form, but in terms of its fractional representation, it cannot be simplified further.
In summary, ( \frac{33}{100} ) is the simplest form of this fraction because the only factor it shares with ( 100 ) is ( 1 ).