Certainly! Let's work through the problem of writing 85% as a fraction in its simplest form.
1. Convert the percentage to a fraction:
- A percentage is another way of representing a fraction with a denominator of 100. So, 85% can be written as:
[tex]\[
85\% = \frac{85}{100}
\][/tex]
2. Simplify the fraction:
- To simplify the fraction [tex]\(\frac{85}{100}\)[/tex], we need to find the greatest common divisor (GCD) of 85 and 100.
3. Find the GCD of 85 and 100:
- The GCD of 85 and 100 is 5.
4. Divide both the numerator and the denominator by the GCD:
- Simplifying [tex]\(\frac{85}{100}\)[/tex] by dividing both the numerator and the denominator by their GCD (which is 5), we get:
[tex]\[
\frac{85 \div 5}{100 \div 5} = \frac{17}{20}
\][/tex]
So, the fraction [tex]\(\frac{85}{100}\)[/tex] simplifies to [tex]\(\frac{17}{20}\)[/tex].
Thus, 85% as a fraction in its simplest form is:
[tex]\[
\boxed{\frac{17}{20}}
\][/tex]
