Knowing how to calculate fractions like 30/480 is a fundamental math skill. This article will guide you through the process of simplifying this fraction and converting it into a percentage, providing a clear understanding of the solution.
Simplifying the Fraction 30/480
The fraction 30/480 represents 30 parts out of a total of 480 parts. To simplify, we need to find the greatest common divisor (GCD) of both 30 and 480. The GCD is the largest number that divides both numbers without leaving a remainder.
One way to find the GCD is to list the factors of each number:
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 480: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 160, 240, 480
The largest number common to both lists is 30.
Therefore, we divide both the numerator (30) and the denominator (480) by 30:
30 ÷ 30 = 1 480 ÷ 30 = 16
This simplifies the fraction 30/480 to 1/16.
Converting the Fraction to a Percentage
To express 1/16 as a percentage, we perform the division:
1 ÷ 16 = 0.0625
To convert this decimal to a percentage, we multiply by 100:
0.0625 x 100 = 6.25%
Therefore, 30/480 is equal to 6.25%.
Understanding the Result
This means that 30 represents 6.25% of 480. Imagine you have 480 apples, and 30 of them are red. The red apples make up 6.25% of the total number of apples.
Practical Applications
Understanding fraction simplification and percentage calculations is crucial in various real-world scenarios, including:
- Calculating discounts: Determining the final price after a percentage discount.
- Analyzing data: Interpreting proportions in statistical data.
- Financial calculations: Calculating interest rates and returns on investments.
- Measurement conversions: Converting between different units of measurement.
By mastering these basic mathematical concepts, you can confidently tackle more complex problems involving fractions and percentages. Remember to always simplify fractions to their lowest terms for easier understanding and calculations.
