there are four options, out of which one is correct.
Choose the correct one.
Which of the following rational numbers is in standard form?

Options

A. `20/30`
B. `10/4`
C. `1/2`
D. `(1)/(-3)`

Answer

To determine which of the given rational numbers is in standard form, we need to check each option to see if the numerator and denominator have any common factors other than 1. A rational number is said to be in standard form if the numerator and denominator are coprime, meaning their greatest common divisor (GCD) is 1.

Let's analyze each option step by step.

### Step 1: Check Option 1 - 20/30
- **Numerator**: 20
- **Denominator**: 30
- **Common Factors**: The common factors of 20 and 30 are 1, 2, 5, and 10.
- **Conclusion**: Since they have common factors other than 1, 20/30 is not in standard form.

### Step 2: Check Option 2 - 8/12
- **Numerator**: 8
- **Denominator**: 12
- **Common Factors**: The common factors of 8 and 12 are 1, 2, and 4.
- **Conclusion**: Since they have common factors other than 1, 8/12 is not in standard form.

### Step 3: Check Option 3 - 1/2
- **Numerator**: 1
- **Denominator**: 2
- **Common Factors**: The only common factor of 1 and 2 is 1.
- **Conclusion**: Since the only common factor is 1, 1/2 is in standard form.

### Step 4: Check Option 4 - 15/25
- **Numerator**: 15
- **Denominator**: 25
- **Common Factors**: The common factors of 15 and 25 are 1 and 5.
- **Conclusion**: Since they have common factors other than 1, 15/25 is not in standard form.

### Final Answer
After checking all options, we find that the only rational number in standard form is **Option 3: 1/2**.

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