20/72 simplified
Understand the Problem
The question is asking for the simplification of the fraction 20/72. To simplify, we need to divide both the numerator and the denominator by their greatest common divisor (GCD).
Answer
The simplified fraction of \( \frac{20}{72} \) is \( \frac{5}{18} \).
Answer for screen readers
The simplified fraction of ( \frac{20}{72} ) is ( \frac{5}{18} ).
Steps to Solve
- Find the GCD of 20 and 72
To simplify the fraction, we first need to find the greatest common divisor (GCD) of the numbers 20 and 72.
The factors of 20 are: 1, 2, 4, 5, 10, 20.
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
The common factors of 20 and 72 are: 1, 2, and 4.
The greatest of these is 4.
Thus, the GCD of 20 and 72 is 4.
- Divide the numerator and denominator by the GCD
Next, we will divide both the numerator (20) and the denominator (72) by their GCD (4).
Calculating the new numerator: $$ \frac{20}{4} = 5 $$
Calculating the new denominator: $$ \frac{72}{4} = 18 $$
- Write the simplified fraction
After dividing both parts, we can express the simplified fraction as: $$ \frac{5}{18} $$
The simplified fraction of ( \frac{20}{72} ) is ( \frac{5}{18} ).
More Information
The process of simplifying fractions helps to express them in their simplest form, making calculations easier. The GCD is crucial in this step, as it ensures that you're dividing by the largest number that can evenly divide both the numerator and the denominator.
Tips
- Not finding the correct GCD: Ensure to list all factors correctly before deciding the GCD.
- Dividing incorrectly: Double-check the division of both the numerator and the denominator to ensure accuracy.
