Difference Calculation: Percentage vs Fraction

This problem requires us to compare two quantities: "65% of 65" and "$\frac{4}{5}$ of 15". We need to find the numerical difference between these two values, specifically how much larger the first quantity is compared to the second.

65% of 65 Calculation

The first step is to calculate the value represented by "65% of 65". To do this, we convert the percentage into a decimal and then multiply it by the number 65.

• Percentage conversion: $65\% = \frac{65}{100} = 0.65$
• Multiplication: $0.65 \times 65$

Let's perform the multiplication:

$0.65 \times 65 = 42.25$

So, the value of 65% of 65 is 42.25.

$\frac{4}{5}$ of 15 Calculation

Next, we calculate the value of "$\frac{4}{5}$ of 15". This involves multiplying the fraction by the number 15.

Calculation:

$ \frac{4}{5} \times 15 $

We can simplify this calculation:

$ \frac{4}{5} \times 15 = \frac{4 \times 15}{5} = \frac{60}{5} = 12 $

Thus, the value of $\frac{4}{5}$ of 15 is 12.

Difference Calculation

The question asks "By how much is 65% of 65 greater than $\frac{4}{5}$ of 15?". This means we need to find the difference between the two calculated values. We subtract the smaller value (12) from the larger value (42.25).

Difference = (Value of 65% of 65) - (Value of $\frac{4}{5}$ of 15)

Performing the subtraction:

$ 42.25 - 12 = 30.25 $

The difference is 30.25.

Final Answer

The calculation shows that 65% of 65 is greater than $\frac{4}{5}$ of 15 by 30.25.