Simplify the following fraction.
`(16)/(24)`

Answer

To simplify the fraction \( \frac{16}{24} \), follow these steps:

### Step 1: Factor the Numerator and Denominator
First, we need to factor both the numerator (16) and the denominator (24) into their prime factors.

- The prime factorization of 16 is:
\[ 16 = 4 \times 4 = 2^2 \times 2^2 = 2^4 \]

- The prime factorization of 24 is:
\[ 24 = 4 \times 6 = 2^2 \times (2 \times 3) = 2^3 \times 3 \]

### Step 2: Write the Fraction with its Factors
Now, we can express the fraction using its prime factors:
\[ \frac{16}{24} = \frac{2^4}{2^3 \times 3} \]

### Step 3: Cancel Common Factors
Next, we can cancel the common factors in the numerator and the denominator. The common factor here is \( 2^3 \):
\[ \frac{2^4}{2^3 \times 3} = \frac{2^{4-3}}{3} = \frac{2^1}{3} = \frac{2}{3} \]

### Step 4: Write the Final Answer
Thus, the simplified form of the fraction \( \frac{16}{24} \) is:
\[ \frac{2}{3} \]