`54 -: 66 -33 = ? `

Options

A. `(1)/(121)`
B. `(2)/(121)`
C. `(4)/(121)`
D. None of these

Answer

To solve the expression \(54 \div 66 - 33\), we will follow the order of operations step by step.

### Step 1: Perform the Division
First, we need to divide \(54\) by \(66\).

\[ \frac{54}{66} \]

### Step 2: Simplify the Fraction
To simplify \(\frac{54}{66}\), we can find the greatest common divisor (GCD) of \(54\) and \(66\). The GCD is \(6\).

\[ \frac{54 \div 6}{66 \div 6} = \frac{9}{11} \]

### Step 3: Substitute Back into the Expression
Now we substitute back into the expression:

\[ \frac{9}{11} - 33 \]

### Step 4: Convert \(33\) to a Fraction
To subtract \(\frac{9}{11}\) from \(33\), we need to express \(33\) as a fraction with a denominator of \(11\):

\[ 33 = \frac{33 \times 11}{11} = \frac{363}{11} \]

### Step 5: Perform the Subtraction
Now we can perform the subtraction:

\[ \frac{9}{11} - \frac{363}{11} = \frac{9 - 363}{11} = \frac{-354}{11} \]

### Step 6: Simplify the Result
Now, we can simplify \(\frac{-354}{11}\):

\[ -354 \div 11 = -32.18 \quad (\text{approximately}) \]

### Final Answer
Thus, the final answer to the expression \(54 \div 66 - 33\) is:

\[ \frac{-354}{11} \quad \text{or approximately } -32.18 \]

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