7/30 simplified
Understand the Problem
The question is asking to simplify the fraction 7/30. The approach involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number.
Answer
The simplified fraction is $\frac{7}{30}$.
Answer for screen readers
The simplified fraction is $\frac{7}{30}$.
Steps to Solve
- Identify the GCD of 7 and 30
To simplify the fraction, we first find the greatest common divisor (GCD) of the numerator (7) and the denominator (30).
The prime factorization of 7 is just 7 (since it's a prime number), and the prime factorization of 30 is $2 \times 3 \times 5$.
Since there are no common factors, the GCD of 7 and 30 is 1.
- Divide by the GCD
Next, we simplify the fraction by dividing both the numerator and the denominator by the GCD.
[ \frac{7}{30} = \frac{7 \div 1}{30 \div 1} = \frac{7}{30} ]
- State the simplified fraction
Since the GCD is 1, the fraction is already in its simplest form.
Thus, the simplified fraction remains:
[ \frac{7}{30} ]
The simplified fraction is $\frac{7}{30}$.
More Information
The fraction $\frac{7}{30}$ is in its simplest form as 7 and 30 have no common factors other than 1. This means that it cannot be simplified further.
Tips
- Mistaking the GCD: Some may miscalculate the GCD and think the fraction can be simplified further. Always verify the GCD by checking the factors.
- Not reducing: Another common mistake is forgetting to divide both the numerator and denominator by the GCD.