Find: `(8)/(9)-(11)/(6)`

Answer

To solve the problem \( \frac{8}{9} - \frac{11}{6} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the Denominators
The denominators are 9 and 6. We need to find the LCM of these two numbers.

- The prime factorization of 9 is \( 3^2 \).
- The prime factorization of 6 is \( 2^1 \times 3^1 \).

To find the LCM, we take the highest power of each prime factor:
- For 2: \( 2^1 \)
- For 3: \( 3^2 \)

Thus, the LCM is:
\[ LCM = 2^1 \times 3^2 = 2 \times 9 = 18 \]

### Step 2: Convert Each Fraction to Have the Same Denominator
Now we will convert both fractions to have a denominator of 18.

1. For \( \frac{8}{9} \):
\[ \frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18} \]

2. For \( \frac{11}{6} \):
\[ \frac{11}{6} = \frac{11 \times 3}{6 \times 3} = \frac{33}{18} \]

### Step 3: Subtract the Two Fractions
Now we can subtract the two fractions:
\[ \frac{16}{18} - \frac{33}{18} = \frac{16 - 33}{18} = \frac{-17}{18} \]

### Step 4: Write the Final Answer
The final answer is:
\[ \frac{8}{9} - \frac{11}{6} = \frac{-17}{18} \]

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