What is 18/30 in simplest form?
The Correct answer and Explanation is:
To simplify the fraction 1830\frac{18}{30}3018, we need to find the greatest common divisor (GCD) of the numerator (18) and the denominator (30). The GCD is the largest number that divides both 18 and 30 without leaving a remainder.
Step 1: Find the GCD of 18 and 30
First, we can list the factors of each number:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Next, we identify the common factors:
- Common Factors: 1, 2, 3, 6
The greatest common factor from this list is 6.
Step 2: Divide both the numerator and the denominator by the GCD
Now that we have the GCD, we can simplify the fraction by dividing both the numerator and the denominator by 6:18÷630÷6=35\frac{18 \div 6}{30 \div 6} = \frac{3}{5}30÷618÷6=53
Thus, the simplest form of 1830\frac{18}{30}3018 is 35\frac{3}{5}53.
Step 3: Verification of Simplification
To ensure that 35\frac{3}{5}53 is indeed in simplest form, we check if there are any common factors between the new numerator and denominator:
- Factors of 3: 1, 3
- Factors of 5: 1, 5
Since the only common factor is 1, we can conclude that 35\frac{3}{5}53 cannot be simplified further.
Conclusion
Therefore, the fraction 1830\frac{18}{30}3018 simplifies to 35\frac{3}{5}53. This process demonstrates the importance of finding the GCD to simplify fractions accurately. Simplifying fractions is crucial in various mathematical applications, making calculations easier and clearer. By breaking down the process into steps—finding the GCD, dividing both the numerator and denominator, and verifying the result—we ensure accurate simplification, enhancing our overall understanding of fraction reduction.