Calculate the Percentage of 21 over 225: Step-by-Step Solution

To find the percentage of 21 over 225, we'll follow these steps:

• Step 1: Express 21 as a fraction of 225: $\frac{21}{225}$.
• Step 2: Simplify the fraction.
• Step 3: Convert the simplified fraction into a percentage by multiplying by 100%.

Now, let's work through each step:

Step 1: The initial fraction is $\frac{21}{225}$.

Step 2: Simplify the fraction. We find the greatest common divisor (GCD) of 21 and 225, which is 3.

Divide both the numerator and the denominator by 3:

$\frac{21 \div 3}{225 \div 3} = \frac{7}{75}$.

Now the fraction is simplified to $\frac{7}{75}$.

Step 3: Convert the simplified fraction into a percentage:

Multiply by 100%: $\frac{7}{75} \times 100\% = \frac{700}{75}\%$.

Simplify $\frac{700}{75}$:

700 divided by 75 equals 9 with a remainder of 25. Thus, $\frac{700}{75} = 9 \frac{25}{75}\%$.

Simplify $\frac{25}{75}$ to $\frac{1}{3}$ (since 25 and 75 can be divided by 25).

Therefore, the percentage is $9 \frac{1}{3}\%$.

The solution to the problem is $9\frac{1}{3}\%$, which corresponds to choice 4.