What is 22.5\% written as a fraction in simplest form? F. \frac{225}{10} G. \frac{45}{100} H. \frac{9}{40} I. \frac{9}{100}
The Correct Answer and Explanation is:
The correct answer is H. \frac{9}{40}.
Here is a step-by-step explanation of how to convert 22.5% into a fraction in its simplest form.
First, it is important to understand what a percentage represents. The word “percent” means “per one hundred.” Therefore, any percentage can be written as a fraction with a denominator of 100. In this case, 22.5% can be written as the fraction \frac{22.5}{100}.
The next step is to eliminate the decimal from the numerator to create a fraction with whole numbers. Since the numerator is 22.5, which has one decimal place, we can multiply both the numerator and the denominator by 10. This is equivalent to multiplying the fraction by \frac{10}{10}, which equals 1, so the value of the fraction remains unchanged.
The calculation is:
\frac{22.5 \times 10}{100 \times 10} = \frac{225}{1000}
Now we have the fraction \frac{225}{1000}, but the question asks for the fraction in its simplest form. To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (225) and the denominator (1000). We can do this by finding common factors and dividing.
We can see that both numbers end in 5 or 0, so they are divisible by 5.
\frac{225 \div 5}{1000 \div 5} = \frac{45}{200}
The resulting fraction, \frac{45}{200}, can be simplified further, as both numbers are still divisible by 5.
\frac{45 \div 5}{200 \div 5} = \frac{9}{40}
To ensure that \frac{9}{40} is in its simplest form, we check for any common factors of 9 and 40. The factors of 9 are 1, 3, and 9. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The only common factor is 1, which means the fraction is fully simplified.
Thus, 22.5% as a fraction in its simplest form is \frac{9}{40}.
