Understanding 37 1/2% as a Fraction and Its Application
In this article, we will break down the process of converting 37 1/2% to a fraction, providing a step-by-step guide and application examples to help you understand the concept better. This knowledge is essential for anyone working with percentages and fractions in their daily lives or in professional settings.
What is 37 1/2%?
37 1/2%, also written as 37.5%, is a specific percentage that can be expressed as a fraction. The term percentage means 'per hundred,' which implies that the value is to be divided by 100. In this article, we'll explore how to convert 37 1/2% to its equivalent fraction and apply the result to a practical problem.
Converting 37 1/2% to a Fraction
1. **Remove the percentage sign**: Start by removing the percentage sign from 37 1/2% to get 37 1/2. Note that 37 1/2 is a mixed number.
2. **Convert the mixed number to an improper fraction**: To convert 37 1/2 to an improper fraction, multiply the whole number (37) by the denominator (2), then add the numerator (1). Place this sum over the original denominator (2): 37times;2 1 74/2.
3. **Divide by 100**: Since the percentage means 'per hundred,' the final step is to divide the fraction by 100: 74/2 ÷ 100 74/200.
Simplifying the Fraction
The fraction 74/200 can be simplified by finding the greatest common divisor (GCD) of 74 and 200, which is 2. Dividing both the numerator and the denominator by 2, we get:
74/200 37/100
To further simplify, we can multiply both the numerator and the denominator by 2 to get:
75/200 3/8
Application Example: What is 37 1/2 of 32?
To find what 37 1/2 of 32 is, we follow these steps:
Step 1: Convert 37 1/2 to a Fraction
We have already determined that 37 1/2% is equal to 3/8.
Step 2: Apply the Fraction to 32
To find 3/8 of 32, multiply 32 by 3/8:
32 x 3/8 (32 x 3) / 8 96 / 8 12
Therefore, 37 1/2 of 32 is 12.
Additional Example: Converting 2/3 of 32
To find 2/3 of 32, we perform the following calculation:
2/3 of 32 2/3 x 32 (32 x 2) / 3 64 / 3 ≈ 21.3333
Expressing Fractions in Simplest Form
Finally, we will convert the fraction 3/8 to its simplest form. The fraction 3/8 is already in its simplest form, as 3 and 8 have no common factors other than 1.
Conclusion
Understanding how to convert percentages to fractions and applying these conversions to practical problems can significantly enhance your numerical and analytical skills. Whether you're a student, a professional, or simply someone looking to improve your math skills, this knowledge is invaluable.