Write the following fractions in simplest form:
`150/(60)`

Answer

To simplify the fraction \( \frac{150}{60} \), we will follow these steps:

### Step 1: Identify the fraction
We start with the fraction:
\[ \frac{150}{60} \]

### Step 2: Find the greatest common divisor (GCD)
To simplify the fraction, we need to find the GCD of the numerator (150) and the denominator (60).

- The factors of 150 are: \( 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 \)
- The factors of 60 are: \( 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 \)

The common factors are \( 1, 2, 3, 5, 6, 10, 15, 30 \). The greatest common factor is \( 30 \).

### Step 3: Divide both numerator and denominator by the GCD
Now, we will divide both the numerator and the denominator by their GCD (30):
\[ \frac{150 \div 30}{60 \div 30} = \frac{5}{2} \]

### Step 4: Check if the fraction is in simplest form
Now we check if \( \frac{5}{2} \) is in simplest form. The factors of 5 are \( 1, 5 \) and the factors of 2 are \( 1, 2 \). The only common factor is \( 1 \), so \( \frac{5}{2} \) is indeed in simplest form.

### Final Answer
Thus, the simplest form of the fraction \( \frac{150}{60} \) is:
\[ \frac{5}{2} \]

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