56 1/4 Percent as a Fraction in Simplest Form
When dealing with mixed percentages, it's essential to understand how to convert them into fractions in their simplest form. In this article, we'll explore how to convert 56 1/4 percent into a fraction in its simplest form.
Converting Mixed Percentages to Fractions
To convert a mixed percentage to a fraction, we need to follow these steps:
- Convert the mixed percentage to an improper fraction: Divide the percentage by 100 to convert it to a decimal, then convert the decimal to an improper fraction.
- Simplify the fraction: Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).
Converting 56 1/4 Percent to a Fraction
Let's apply the above steps to convert 56 1/4 percent to a fraction:
Step 1: Convert the mixed percentage to an improper fraction
Divide 56 1/4 by 100:
56 1/4 ÷ 100 = 1.40625
Now, convert the decimal to an improper fraction:
1.40625 = 113/80 + 1/4 = 113/80 + 1/4 = (113 + 1/4) / 1 = 113.25 / 1
To convert the mixed number to an improper fraction, multiply the whole number part (113) by the denominator (1) and add the numerator (1):
= (113 × 1 + 1) / 1 = 114.25 / 1
Step 2: Simplify the fraction
To simplify the fraction, we need to find the GCD of the numerator and denominator:
GCD(114.25, 1) = 1
Since the GCD is 1, the fraction is already in its simplest form:
56 1/4 percent as a fraction in simplest form is 227/4
Therefore, the simplest form of the fraction equivalent to 56 1/4 percent is 227/4.
