`1095/(1168)` in simplest form is-

Options

A. `13/16`
B. `15/(16)`
C. `17/26`
D. `25/26`

Answer

To simplify the fraction \( \frac{1095}{1168} \), we will follow these steps:

### Step 1: Factor both numbers
First, we need to find the prime factorization of both 1095 and 1168.

- For 1095:
- Divide by 5: \( 1095 \div 5 = 219 \)
- Next, factor 219: \( 219 \div 3 = 73 \)
- So, \( 1095 = 5 \times 3 \times 73 \)

- For 1168:
- Divide by 2: \( 1168 \div 2 = 584 \)
- Divide by 2 again: \( 584 \div 2 = 292 \)
- Divide by 2 again: \( 292 \div 2 = 146 \)
- Divide by 2 again: \( 146 \div 2 = 73 \)
- So, \( 1168 = 2^4 \times 73 \)

### Step 2: Write the fraction with the factorizations
Now we can rewrite the fraction:
\[ \frac{1095}{1168} = \frac{5 \times 3 \times 73}{2^4 \times 73} \]

### Step 3: Cancel the common factors
Both the numerator and the denominator have a common factor of 73. We can cancel this out:
\[ \frac{5 \times 3 \times \cancel{73}}{2^4 \times \cancel{73}} = \frac{5 \times 3}{2^4} = \frac{15}{16} \]

### Step 4: Write the final answer
Thus, the simplest form of \( \frac{1095}{1168} \) is:
\[ \frac{15}{16} \]