Write 58% as a fraction in simplest form
The Correct Answer and Explanation is:
Correct Answer:
58% as a fraction in simplest form is2950\frac{29}{50}5029
Explanation
To convert a percentage to a fraction, follow a step-by-step process. Let’s break down the conversion of 58% into a fraction and simplify it.
Step 1: Understand the meaning of a percentage
The word “percent” means “per hundred.” So, 58% means 58 out of 100 or:58%=5810058\% = \frac{58}{100}58%=10058
Step 2: Simplify the fraction
Now that we have the fraction 58100\frac{58}{100}10058, we simplify it by finding the greatest common divisor (GCD) of the numerator (58) and the denominator (100).
First, list the factors:
- Factors of 58: 1, 2, 29, 58
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The greatest common factor they share is 2.
So divide both the numerator and the denominator by 2:58÷2100÷2=2950\frac{58 ÷ 2}{100 ÷ 2} = \frac{29}{50}100÷258÷2=5029
Step 3: Check if the fraction is in simplest form
Now we have 2950\frac{29}{50}5029. Let’s check:
- 29 is a prime number, meaning it has no divisors other than 1 and itself.
- 50’s only prime factors are 2 and 5.
Since 29 and 50 share no common factors other than 1, this fraction is already in simplest form.
Conclusion:
58% written as a fraction is 58100\frac{58}{100}10058, which simplifies to 2950\frac{29}{50}5029. This final form is the simplest version because the numerator and the denominator have no common factors other than 1. Converting percentages to fractions is a helpful skill in math, especially when comparing values or solving real-world problems involving ratios.
