What is 65% written as a fraction in its simplest form?
0000
13
The Correct Answer and Explanation is:
To express 65% as a fraction in its simplest form, we start by understanding what 65% means. The percent symbol (%) signifies “per hundred,” so 65% is equivalent to 65 per 100, or ( \frac{65}{100} ).
Step 1: Write 65% as a Fraction
Since 65% means 65 out of 100, we can directly write it as:
[
\frac{65}{100}
]
Step 2: Simplify the Fraction
To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator (65) and the denominator (100). The GCD is the largest number that divides both numbers without leaving a remainder.
Finding the GCD of 65 and 100:
- Prime factorization of 65: ( 65 = 5 \times 13 )
- Prime factorization of 100: ( 100 = 2 \times 2 \times 5 \times 5 )
The common factor between these numbers is 5.
Dividing the numerator and denominator by 5:
[
\frac{65 \div 5}{100 \div 5} = \frac{13}{20}
]
Therefore, 65% as a fraction in its simplest form is:
[
\frac{13}{20}
]
Explanation of Simplification
Simplifying a fraction involves dividing both the numerator and denominator by their GCD, which reduces the fraction to its lowest terms without changing its value. In this case, dividing by 5 removes common factors, resulting in the fraction ( \frac{13}{20} ), which cannot be simplified further because 13 and 20 have no common divisors other than 1.
Final Answer
Thus, 65% written as a fraction in its simplest form is:
[
\frac{13}{20}
]
Understanding this process is helpful when working with percentages, as it allows you to convert them to fractions for various applications, such as solving problems in math, science, and finance where fractional representations are required for precision.