Reduce `(96)/( 128)` to its simplest form.

Answer

To reduce the fraction \( \frac{96}{128} \) to its simplest form, we will follow these steps:

### Step 1: Identify the Greatest Common Divisor (GCD)
First, we need to find the GCD of the numerator (96) and the denominator (128). The GCD is the largest number that divides both numbers without leaving a remainder.

### Step 2: Divide by the GCD
Once we have the GCD, we will divide both the numerator and the denominator by this number.

### Step 3: Simplify the Fraction
After dividing, we will write the simplified fraction.

### Detailed Solution:

1. **Finding the GCD of 96 and 128:**
- The factors of 96 are: \( 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 \)
- The factors of 128 are: \( 1, 2, 4, 8, 16, 32, 64, 128 \)
- The common factors are: \( 1, 2, 4, 8, 16 \)
- The greatest common factor is \( 16 \).

2. **Dividing the numerator and denominator by the GCD:**
\[ \frac{96 \div 16}{128 \div 16} = \frac{6}{8} \]

3. **Finding the GCD of 6 and 8:**
- The factors of 6 are: \( 1, 2, 3, 6 \)
- The factors of 8 are: \( 1, 2, 4, 8 \)
- The common factors are: \( 1, 2 \)
- The greatest common factor is \( 2 \).

4. **Dividing the new numerator and denominator by the GCD:**
\[ \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \]

### Final Answer:
The simplest form of \( \frac{96}{128} \) is \( \frac{3}{4} \).

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