What percent of 12 is 9?
The Correct Answer and Explanation is:
To determine what percentage 9 is of 12, we can use the formula for calculating percentages:
[
\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100
]
In this scenario, the part is 9 (the number we want to find the percentage of), and the whole is 12 (the number we are comparing it to). Plugging these values into the formula gives us:
[
\text{Percentage} = \left(\frac{9}{12}\right) \times 100
]
First, we simplify the fraction (\frac{9}{12}). Both numbers can be divided by their greatest common divisor (GCD), which is 3:
[
\frac{9 \div 3}{12 \div 3} = \frac{3}{4}
]
Now we can convert the simplified fraction into a percentage:
[
\text{Percentage} = \left(\frac{3}{4}\right) \times 100
]
Calculating this gives:
[
\frac{3}{4} = 0.75
]
Then, multiplying by 100 yields:
[
0.75 \times 100 = 75
]
Thus, 9 is 75% of 12.
Explanation of the Calculation
The concept of percentages is crucial in various fields, including mathematics, finance, and everyday life. Percentages provide a way to compare quantities relative to a whole. In our example, we wanted to see how much of the total number (12) was made up by another number (9).
By representing the relationship between the two numbers as a fraction, we can better understand their relationship. The fraction (\frac{9}{12}) gives us a clear visual of how 9 relates to 12 as parts of a whole. Simplifying this fraction makes calculations easier and more intuitive, allowing us to see that 9 is three-quarters of 12.
Furthermore, converting the fraction to a decimal and then multiplying by 100 makes it clear that we are expressing this relationship in terms of a percentage, which is a standard way of conveying information about proportions. Hence, the result, 75%, indicates that 9 constitutes three-quarters of 12.