27/99 simplified
Understand the Problem
The question is asking to simplify the fraction 27/99 to its lowest terms, which involves finding the greatest common divisor (GCD) of the numerator and the denominator.
Answer
The simplified fraction is $\frac{3}{11}$.
Answer for screen readers
The simplified fraction of $\frac{27}{99}$ is $\frac{3}{11}$.
Steps to Solve
- Find the GCD of 27 and 99
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (27) and the denominator (99). The GCD is the largest number that divides both 27 and 99 without leaving a remainder.
- List the factors of 27 and 99
The factors of 27 are: 1, 3, 9, 27
The factors of 99 are: 1, 3, 9, 11, 33, 99
- Identify the GCD
From the list of factors, we see that the GCD of 27 and 99 is 9, since it is the largest common factor.
- Divide the numerator and denominator by the GCD
Now we can simplify the fraction by dividing both the numerator and the denominator by the GCD (9).
$$ \frac{27 \div 9}{99 \div 9} = \frac{3}{11} $$
Now the fraction 27/99 is simplified to 3/11.
The simplified fraction of $\frac{27}{99}$ is $\frac{3}{11}$.
More Information
Simplifying fractions is important in mathematics for expressing values in their simplest form. Using the GCD helps in reducing fractions correctly. Additionally, both 3 and 11 are prime numbers, meaning this fraction cannot be simplified further.
Tips
- Forgetting to find the GCD properly, which can lead to incorrect simplification.
- Not dividing both the numerator and denominator by the GCD when simplifying.
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