If a and b are rational numbers `a: b` is equal to:

Options

A. `-2 : 1`
B. `2:1`
C. `sqrt(3):1`
D. `-sqrt(3):1`

Answer

To solve the question "If a and b are rational numbers, what is the ratio a:b?", we need to understand the definition of rational numbers and how ratios work.

### Step-by-Step Solution:

1. **Understanding Rational Numbers**:
- A rational number is defined as any number that can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
- Examples of rational numbers include \( \frac{1}{2}, -\frac{3}{4}, 5, 0 \) (which can be written as \( \frac{0}{1} \)), etc.

**Hint**: Recall that rational numbers can be positive or negative, and they can also be whole numbers.

2. **Expressing the Ratio**:
- The ratio \( a:b \) means \( \frac{a}{b} \).
- Since both \( a \) and \( b \) are rational numbers, we can express them as \( a = \frac{p_1}{q_1} \) and \( b = \frac{p_2}{q_2} \), where \( p_1, p_2, q_1, q_2 \) are integers and \( q_1, q_2 \neq 0 \).

**Hint**: Remember that a ratio compares two quantities and can be simplified.

3. **Finding the Ratio**:
- The ratio \( a:b \) can be calculated as:
\[ a:b = \frac{a}{b} = \frac{\frac{p_1}{q_1}}{\frac{p_2}{q_2}} = \frac{p_1 \cdot q_2}{p_2 \cdot q_1} \]
- This shows that the ratio \( a:b \) is also a rational number, as it is expressed as the quotient of two integers.

**Hint**: When dividing fractions, remember to multiply by the reciprocal.

4. **Conclusion**:
- Therefore, the ratio \( a:b \) is a rational number since it can be expressed in the form \( \frac{p}{q} \) where both \( p \) and \( q \) are integers.

**Hint**: Always check if the final answer can be simplified to its lowest terms.

### Final Answer:
The ratio \( a:b \) is a rational number.