18/99 simplified
Understand the Problem
The question is asking to simplify the fraction 18/99 to its lowest terms. This involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
Answer
The simplified fraction is \( \frac{2}{11} \).
Answer for screen readers
The simplified form of the fraction ( \frac{18}{99} ) is ( \frac{2}{11} ).
Steps to Solve
- Find the GCD of 18 and 99
To simplify the fraction, we first need to find the greatest common divisor (GCD) of the numerator (18) and the denominator (99). We can use the prime factorization method or the Euclidean algorithm.
For 18, the prime factors are: $$ 18 = 2 \times 3^2 $$
For 99, the prime factors are: $$ 99 = 3^2 \times 11 $$
The common factor here is (3^2 = 9), so the GCD is 9.
- Divide both the numerator and the denominator by the GCD
Now that we have the GCD (9), we divide both the numerator and the denominator by 9 to simplify the fraction:
$$ \text{Numerator: } \frac{18}{9} = 2 $$
$$ \text{Denominator: } \frac{99}{9} = 11 $$
Thus, the simplified form of the fraction is:
$$ \frac{2}{11} $$
The simplified form of the fraction ( \frac{18}{99} ) is ( \frac{2}{11} ).
More Information
The fraction ( \frac{18}{99} ) simplifies down to ( \frac{2}{11} ), which means for every 18 parts of something, there are 99 parts total, it can be reduced to 2 parts of 11 total parts.
Tips
- Forgetting to divide both the numerator and the denominator by the GCD. This can lead to an incorrect simplified fraction.
- Miscalculating the GCD, leading to incorrect results. Always double-check the factorization or the GCD calculation.
