How do you write 56% as a fraction in simplest form?
The Correct Answer and Explanation is :
To write 56% as a fraction in simplest form, we follow these steps:
Step 1: Understand the percentage as a fraction
A percentage is simply a number out of 100. Therefore, 56% means 56 out of 100, which can be written as:
[
\frac{56}{100}
]
Step 2: Simplify the fraction
To simplify the fraction, we need to divide both the numerator (56) and the denominator (100) by their greatest common divisor (GCD). The GCD is the largest number that can divide both 56 and 100.
- Find the factors of 56: The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
- Find the factors of 100: The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
- Identify the GCD: The largest common factor between 56 and 100 is 4.
Step 3: Divide both the numerator and denominator by the GCD
Now, divide both 56 and 100 by their GCD, which is 4:
[
\frac{56 \div 4}{100 \div 4} = \frac{14}{25}
]
Step 4: Conclusion
Thus, the simplest form of the fraction equivalent to 56% is:
[
\frac{14}{25}
]
Explanation
This process of converting a percentage to a fraction involves two key concepts: understanding that a percentage is a ratio out of 100 and simplifying fractions. Percentages are often used because they provide an easy way to compare parts to a whole. By converting the percentage into a fraction and simplifying it, we make the number easier to work with in various mathematical operations, such as addition, subtraction, or multiplication of fractions.
Converting percentages to fractions also helps in real-life scenarios, such as calculating discounts, tax rates, and interest rates, where percentages are common. Simplifying the fraction further ensures that we work with the smallest possible values for easier computation.