what is 33/50 simplified

2 min read 10-03-2025

The fraction 33/50 represents 33 parts out of a total of 50 equal parts. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator (33) and the denominator (50) and divide both by it. Let's explore how to simplify 33/50.

Finding the Greatest Common Divisor (GCD)

The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. To find the GCD of 33 and 50, we can use a method called prime factorization.

Prime Factorization of 33

33 can be broken down into its prime factors as 3 x 11. Prime numbers are whole numbers greater than 1 that are only divisible by 1 and themselves.

Prime Factorization of 50

50's prime factorization is 2 x 5 x 5, or 2 x 5².

Identifying Common Factors

Comparing the prime factorizations of 33 (3 x 11) and 50 (2 x 5²), we see that they don't share any common prime factors. This means their GCD is 1.

Simplifying the Fraction

Since the GCD of 33 and 50 is 1, we can't simplify the fraction any further. Dividing both the numerator and denominator by 1 doesn't change the fraction's value.

Therefore, 33/50 is already in its simplest form.

There's no simpler way to represent the ratio of 33 to 50. It remains as 33/50.

Converting to Decimal

While we can't simplify the fraction further, we can convert it to a decimal for easier understanding. To do this, simply divide the numerator (33) by the denominator (50):

33 ÷ 50 = 0.66

So, 33/50 is equivalent to 0.66.

Converting to Percentage

Another way to express 33/50 is as a percentage. Since a percentage is a fraction out of 100, we can multiply the decimal equivalent by 100:

0.66 x 100 = 66%

Therefore, 33/50 is equal to 66%.

This comprehensive explanation should clarify why 33/50 is already in its simplest form and provide alternative representations of the fraction. Remember, simplifying a fraction involves finding the greatest common divisor and dividing both the numerator and denominator by it. If the GCD is 1, as in this case, the fraction is already simplified.