Express the fractions in their simplest forms:
`18/(117)`

Options

A. `7/(17)`
B. `3/(23)`
C. `2/(11)`
D. `2/(13)`

Answer

To express the fraction \( \frac{18}{117} \) in its simplest form, follow these steps:

### Step 1: Factor the Numerator and Denominator
First, we need to factor both the numerator (18) and the denominator (117).

- The number 18 can be factored as:
\[ 18 = 2 \times 9 \]
- The number 117 can be factored as:
\[ 117 = 13 \times 9 \]

### Step 2: Write the Fraction with Factors
Now we can rewrite the fraction using the factors we found:
\[ \frac{18}{117} = \frac{2 \times 9}{13 \times 9} \]

### Step 3: Cancel Common Factors
Next, we can cancel the common factor of 9 from the numerator and the denominator:
\[ \frac{2 \times \cancel{9}}{13 \times \cancel{9}} = \frac{2}{13} \]

### Step 4: Write the Simplified Fraction
Now we have simplified the fraction to:
\[ \frac{2}{13} \]

### Conclusion
Thus, the simplest form of the fraction \( \frac{18}{117} \) is:
\[ \frac{2}{13} \]

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