Express 15.75 in the form of `p/q`

Answer

To express 15.75 in the form of \( \frac{p}{q} \), we can follow these steps:

### Step 1: Write the number without the decimal point
We start with the number 15.75. To eliminate the decimal, we can multiply both the numerator and denominator by 100 (since there are two digits after the decimal point).

\[ 15.75 = \frac{15.75 \times 100}{100} = \frac{1575}{100} \]

### Step 2: Simplify the fraction
Now we need to simplify the fraction \( \frac{1575}{100} \). We can do this by finding the greatest common divisor (GCD) of 1575 and 100.

First, we can factor both numbers:
- \( 1575 = 3 \times 5^2 \times 63 = 3 \times 5^2 \times 3 \times 21 = 3^2 \times 5^2 \times 7 \)
- \( 100 = 10^2 = 2^2 \times 5^2 \)

The common factors are \( 5^2 \).

### Step 3: Divide both the numerator and denominator by their GCD
Now, we divide both the numerator and denominator by \( 25 \) (which is \( 5^2 \)):

\[ \frac{1575 \div 25}{100 \div 25} = \frac{63}{4} \]

### Final Answer
Thus, we can express 15.75 in the form of \( \frac{p}{q} \) as:

\[ \frac{63}{4} \]

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