Converting 37 1/2 to a Fraction: A Comprehensive Guide

In this article, we will explore the process of converting the mixed number 37 1/2 into a fraction. This guide will cover various methods and steps to ensure a thorough understanding.

Step-by-Step Conversion

Let's start with the mixed number 37 1/2 and convert it into a fraction.

1. Convert to an Improper Fraction

First, we convert the mixed number to an improper fraction. The general form of a mixed number is n sfrac{a}{b}, where n is the whole number, a is the numerator, and b is the denominator.

37 1/2 can be rewritten as:

37 1/2

To add these, we convert the whole number 37 to a fraction with the same denominator as the fractional part:

37 37/1

Now, we get a common denominator. The common denominator for 1 and 2 is 2. So, we convert 37/1 to 74/2 (since 37*2 74).

Therefore, 37 1/2 can be written as:

74/2 1/2 75/2

2. Convert the Percentage to a Fraction

Now, let's see how to convert a percentage to a fraction. For this, we'll use the mixed number 37 1/2 as 37.5%.

To convert a percentage to a fraction, we divide the percentage by 100.

37.5% 37.5/100

Multiplying the numerator and the denominator by 2 to eliminate the decimal:

37.5/100 * 2/2 75/200

Simplifying the fraction by dividing both the numerator and the denominator by 25:

75/200 3/8

3. Simplification and Verification

Our final simplified fraction is 3/8.

Let's verify this by using a different method. Starting with 37 1/2 again, we convert it directly to a fraction:

37 1/2 37.5

Since 37.5 375/10, we can simplify this further:

375/10 75/20

Multiplying both the numerator and the denominator by 5 to get to 200:

75/20 * 5/5 375/100

This can be further simplified to:

375/100 75/200 3/8

Conclusion

Through these steps, we have successfully converted the mixed number 37 1/2 to the fraction 3/8. Whether you follow the step of converting it to an improper fraction or directly convert 37.5% to a fraction, the result remains the same.

Further Reading

If you are interested in learning more about fractions and percentages, you might find the following articles useful:

Converting Fractions to Decimals and Percentages Understanding and Solving Fractional Equations Fractions in Real-World Applications

By mastering these concepts, you will be well-equipped to handle various mathematical problems involving fractions and percentages.

Keywords

Keywords: fraction, mixed number, percentage