Express the fractions in their simplest forms:
`30/(54)`

Answer

To express the fraction \( \frac{30}{54} \) in its simplest form, follow these steps:

### Step 1: Factor the numerator and denominator
First, we need to factor both the numerator (30) and the denominator (54) into their prime factors.

- The number 30 can be factored as:
\[ 30 = 2 \times 3 \times 5 \]

- The number 54 can be factored as:
\[ 54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^3 \]

### Step 2: Write the fraction using the factors
Now, we can rewrite the fraction using these factors:
\[ \frac{30}{54} = \frac{2 \times 3 \times 5}{2 \times 3^3} \]

### Step 3: Cancel the common factors
Next, we look for common factors in the numerator and the denominator. Here, both have \( 2 \) and \( 3 \) as common factors.

- Cancel the \( 2 \):
\[ \frac{2 \times 3 \times 5}{2 \times 3^3} = \frac{3 \times 5}{3^3} \]

- Cancel one \( 3 \):
\[ \frac{3 \times 5}{3 \times 3^2} = \frac{5}{3^2} \]

### Step 4: Simplify the fraction
Now we can simplify the fraction further:
\[ \frac{5}{3^2} = \frac{5}{9} \]

### Final Answer
Thus, the simplest form of the fraction \( \frac{30}{54} \) is:
\[ \frac{5}{9} \]

---