What is 30/270? Understanding Fractions and Simplification
The question "What is 30/270?" asks us to find the result of dividing 30 by 270. This is a simple fraction that can be simplified to a more manageable form. Let's explore how to solve this and understand the underlying concepts.
Calculating the Fraction
The simplest way to approach this is through direct division: 30 divided by 270 equals 0.11111... This is a repeating decimal. However, in many contexts, representing the answer as a simplified fraction is more useful and precise.
Simplifying the Fraction
To simplify 30/270, we need to find the greatest common divisor (GCD) of both the numerator (30) and the denominator (270). The GCD is the largest number that divides both 30 and 270 without leaving a remainder.
One way to find the GCD is by listing the factors of each number:
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 270: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The largest number that appears in both lists is 30. Therefore, the GCD of 30 and 270 is 30.
Now, we divide both the numerator and the denominator by the GCD:
30 ÷ 30 = 1 270 ÷ 30 = 9
Therefore, the simplified fraction is 1/9.
Conclusion
30/270 is equivalent to 1/9. This simplified fraction provides a clearer and more concise representation of the original fraction. Understanding how to simplify fractions is a fundamental skill in mathematics and has applications across various fields.
