What is 75/100 in simplest form?
Understand the Problem
The question is asking how to simplify the fraction 75/100 to its simplest form. This involves finding the greatest common divisor (GCD) of 75 and 100 and then dividing both the numerator and the denominator by that GCD.
Answer
The simplest form of the fraction $\frac{75}{100}$ is $\frac{3}{4}$.
Answer for screen readers
The simplest form of the fraction $\frac{75}{100}$ is $\frac{3}{4}$.
Steps to Solve
- Find the GCD of 75 and 100
To simplify the fraction, we start by finding the greatest common divisor (GCD) of 75 and 100. The GCD is the largest number that divides both numbers evenly.
The factors of 75 are: 1, 3, 5, 15, 25, 75
The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100
The common factors are 1, 5, and 25. So, the GCD is 25.
- Divide both the numerator and the denominator by the GCD
Now that we found the GCD, we can simplify the fraction.
We divide the numerator (75) and the denominator (100) by the GCD (25):
$$ \frac{75 \div 25}{100 \div 25} $$
This simplifies to:
$$ \frac{3}{4} $$
- State the simplified fraction
Now we can clearly state the simplified form of the original fraction.
The simplified fraction of $\frac{75}{100}$ is $\frac{3}{4}$.
The simplest form of the fraction $\frac{75}{100}$ is $\frac{3}{4}$.
More Information
Simplifying fractions is a common part of math that helps to present ratios in a clearer form. When you simplify $\frac{75}{100}$ to $\frac{3}{4}$, it indicates that both numbers share the same proportion even though they look different.
Tips
- Forgetting to check for the largest common factor, which can lead to not simplifying the fraction enough.
- Confusing the process of finding GCD with other methods such as just reducing the fraction by subtracting or adding.
