110% as a fraction in simplest form
The Correct Answer and Explanation is:
To convert 110% into a fraction in its simplest form, we follow a few straightforward steps.
Step 1: Express as a fraction
First, we recognize that percent means per hundred. Therefore, 110% can be written as:
[
\text{110%} = \frac{110}{100}
]
This means 110 percent is equivalent to the fraction ( \frac{110}{100} ).
Step 2: Simplify the fraction
To simplify the fraction, we look for the greatest common divisor (GCD) of the numerator (110) and the denominator (100). The GCD of 110 and 100 is 10, which is the largest number that divides both 110 and 100 without leaving a remainder.
Now, divide both the numerator and denominator by 10:
[
\frac{110}{100} = \frac{110 \div 10}{100 \div 10} = \frac{11}{10}
]
So, 110% as a fraction in its simplest form is ( \frac{11}{10} ).
Step 3: Check the result
The fraction ( \frac{11}{10} ) is in its simplest form because 11 and 10 have no common factors other than 1. Additionally, since 110% represents a value greater than 100%, the fraction ( \frac{11}{10} ) makes sense, as it is greater than 1.
Explanation of the process
- Percent means “per hundred,” so 110% is just 110 out of 100.
- Simplifying the fraction involves finding the GCD of 110 and 100, which is 10. By dividing both the numerator and denominator by 10, we reduce the fraction to its simplest form.
- This approach applies to any percent to fraction conversion: write the percent as a fraction out of 100, then simplify by dividing both the numerator and the denominator by their GCD.
Thus, 110% is equivalent to ( \frac{11}{10} ) when expressed as a fraction in its simplest form.