Express each of the following as a fraction :
`165%`

Answer

To express 165% as a fraction, we can follow these steps:

### Step 1: Understand the concept of percentage
Percentage means "per hundred." Therefore, 165% can be expressed as:
\[ 165\% = \frac{165}{100} \]

### Step 2: Simplify the fraction
Now, we need to simplify the fraction \(\frac{165}{100}\). We can do this by finding the greatest common divisor (GCD) of 165 and 100.

- The factors of 165 are: 1, 3, 5, 11, 15, 33, 55, 165
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100

The GCD of 165 and 100 is 5.

### Step 3: Divide both the numerator and the denominator by the GCD
Now, we divide both the numerator and the denominator by 5:
\[ \frac{165 \div 5}{100 \div 5} = \frac{33}{20} \]

### Step 4: Convert to a mixed number (optional)
To convert \(\frac{33}{20}\) into a mixed number, we divide 33 by 20:
- 20 goes into 33 one time (1), with a remainder of 13.

So, we can express it as:
\[ 1 \frac{13}{20} \]

### Final Answer
Thus, \(165\%\) can be expressed as the fraction \(\frac{33}{20}\) or as the mixed number \(1 \frac{13}{20}\).

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