Express the fractions in their simplest forms:
`64/(96)`

Answer

To express the fraction \( \frac{64}{96} \) in its simplest form, we can follow these steps:

### Step 1: Find the prime factors of 64
- Start dividing 64 by the smallest prime number, which is 2.
- \( 64 \div 2 = 32 \)
- \( 32 \div 2 = 16 \)
- \( 16 \div 2 = 8 \)
- \( 8 \div 2 = 4 \)
- \( 4 \div 2 = 2 \)
- \( 2 \div 2 = 1 \)
- The prime factorization of 64 is \( 2^6 \) (since we divided by 2 a total of 6 times).

### Step 2: Find the prime factors of 96
- Now, divide 96 by 2.
- \( 96 \div 2 = 48 \)
- \( 48 \div 2 = 24 \)
- \( 24 \div 2 = 12 \)
- \( 12 \div 2 = 6 \)
- \( 6 \div 2 = 3 \)
- \( 3 \div 3 = 1 \)
- The prime factorization of 96 is \( 2^5 \times 3^1 \) (since we divided by 2 a total of 5 times and then by 3 once).

### Step 3: Write the fraction using the prime factors
- Now we can rewrite the fraction \( \frac{64}{96} \) using its prime factors:
\[ \frac{64}{96} = \frac{2^6}{2^5 \times 3^1} \]

### Step 4: Simplify the fraction
- We can cancel out the common factors in the numerator and the denominator:
\[ \frac{2^6}{2^5 \times 3^1} = \frac{2^{6-5}}{3^1} = \frac{2^1}{3^1} = \frac{2}{3} \]

### Final Answer
- The fraction \( \frac{64}{96} \) in its simplest form is \( \frac{2}{3} \).

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