Reduce the following fractions to simplest form :
`18/81`

Answer

To reduce the fraction \( \frac{18}{81} \) to its simplest form, follow these steps:

### Step 1: Identify the Greatest Common Divisor (GCD)
First, we need to find the GCD of the numerator (18) and the denominator (81). The GCD is the largest number that divides both numbers without leaving a remainder.

### Step 2: Factor the Numbers
- The factors of 18 are: \( 1, 2, 3, 6, 9, 18 \)
- The factors of 81 are: \( 1, 3, 9, 27, 81 \)

From the factors, we can see that the common factors are \( 1, 3, 9 \). The greatest of these is 9.

### Step 3: Divide the Numerator and Denominator by the GCD
Now, we divide both the numerator and the denominator by their GCD (9):

\[ \frac{18 \div 9}{81 \div 9} = \frac{2}{9} \]

### Step 4: Check for Further Simplification
Now we need to check if \( \frac{2}{9} \) can be simplified further. The factors of 2 are \( 1, 2 \) and the factors of 9 are \( 1, 3, 9 \). The only common factor is 1, which means \( \frac{2}{9} \) is already in its simplest form.

### Final Answer
Thus, the simplest form of the fraction \( \frac{18}{81} \) is \( \frac{2}{9} \).

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