Express the fractions in their simplest forms:
`24/(32)`

Answer

To express the fraction \( \frac{24}{32} \) in its simplest form, follow these steps:

### Step 1: Factorize the Numerator and Denominator
First, we need to factorize both the numerator (24) and the denominator (32).

- **Numerator (24)**:
- \( 24 = 2 \times 12 \)
- \( 12 = 2 \times 6 \)
- \( 6 = 2 \times 3 \)

So, \( 24 = 2^3 \times 3 \).

- **Denominator (32)**:
- \( 32 = 2 \times 16 \)
- \( 16 = 2 \times 8 \)
- \( 8 = 2 \times 4 \)
- \( 4 = 2 \times 2 \)

So, \( 32 = 2^5 \).

### Step 2: Write the Fraction with the Factors
Now we can rewrite the fraction using the factors we found:
\[ \frac{24}{32} = \frac{2^3 \times 3}{2^5} \]

### Step 3: Simplify the Fraction
Next, we can simplify the fraction by canceling out the common factors in the numerator and the denominator.

- The common factor is \( 2^3 \):
\[ \frac{2^3 \times 3}{2^5} = \frac{3}{2^{5-3}} = \frac{3}{2^2} = \frac{3}{4} \]

### Step 4: Final Answer
Thus, the simplest form of the fraction \( \frac{24}{32} \) is:
\[ \frac{3}{4} \]

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