What is 75/100 in simplest form?
Understand the Problem
The question is asking for the simplest form of the fraction 75/100, which involves reducing it to its lowest terms by finding the greatest common divisor (GCD) of the numerator and denominator.
Answer
The simplest form of the fraction is $\frac{3}{4}$.
Answer for screen readers
The simplest form of the fraction $\frac{75}{100}$ is $\frac{3}{4}$.
Steps to Solve
- Identify the numerator and denominator
The numerator is 75 and the denominator is 100.
- Find the GCD of 75 and 100
To find the greatest common divisor (GCD), we can list the factors for both numbers:
- Factors of 75: 1, 3, 5, 15, 25, 75
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The common factors are 1, 5, and 25. The greatest of these is 25.
- Divide both the numerator and the denominator by the GCD
Now we divide both by 25:
$$ \frac{75 \div 25}{100 \div 25} = \frac{3}{4} $$
- Write the simplest form
The fraction $ \frac{75}{100} $ is now simplified to $ \frac{3}{4} $.
The simplest form of the fraction $\frac{75}{100}$ is $\frac{3}{4}$.
More Information
To simplify fractions, you can always find the GCD of the numerator and the denominator to reduce the fraction to its lowest terms. In this case, both 75 and 100 can be divided evenly by 25.
Tips
- Forgetting to find the GCD and simply dividing without ensuring it's the largest common factor can lead to incorrect simplifications.
- Not checking if the result is in its simplest form can also be a mistake. Always ensure that the numerator and denominator have no common factors besides 1.