Write `(55)/(-66)`in simplified form

Options

A. `(6)/(-5)`
B. `(-5)/(6)`
C. `(-55)/(66)`
D. none of these

Answer

To simplify the fraction \( \frac{55}{-66} \), follow these steps:

### Step 1: Identify the numerator and denominator
The numerator is \( 55 \) and the denominator is \( -66 \).

### Step 2: Factor the denominator
The denominator \( -66 \) can be factored as:
\[ -66 = -1 \times 66 = -1 \times (6 \times 11) \]

### Step 3: Factor the numerator
The numerator \( 55 \) can be factored as:
\[ 55 = 5 \times 11 \]

### Step 4: Rewrite the fraction with factored terms
Now, we can rewrite the fraction:
\[ \frac{55}{-66} = \frac{5 \times 11}{-1 \times 6 \times 11} \]

### Step 5: Cancel the common factors
The common factor \( 11 \) in the numerator and denominator can be canceled:
\[ \frac{5 \times \cancel{11}}{-1 \times 6 \times \cancel{11}} = \frac{5}{-6} \]

### Step 6: Write the simplified form
The simplified form of the fraction is:
\[ \frac{5}{-6} \]
This can also be expressed as:
\[ -\frac{5}{6} \]

### Final Answer
Thus, the simplified form of \( \frac{55}{-66} \) is:
\[ -\frac{5}{6} \]

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