Ratio in Simplest Form

The concept of simplifying ratios involves finding the simplest form of the given ratio. A ratio is said to be in its simplest form when there are no common factors between the numerator and the denominator.

Explanation:

1. Definition of a Ratio:
- A ratio is a comparison of two or more quantities.
- It is expressed as a fraction or with a colon (:).

2. Simplest Form of a Ratio:
- To simplify a ratio, you need to divide both the numerator and the denominator by their greatest common factor (GCF).
- The GCF is the largest number that divides evenly into both the numerator and the denominator.

3. Common Factors:
- Common factors are the numbers that can divide two or more numbers without leaving a remainder.
- For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

4. Finding the Simplest Form:
- To find the simplest form of a ratio, we need to divide both the numerator and the denominator by their GCF.
- By doing so, we eliminate any common factors and obtain a ratio with no common factor.
- This means that the numerator and denominator are relatively prime or coprime.

5. Importance of Simplest Form:
- Expressing a ratio in its simplest form makes it easier to understand and work with.
- It provides a clear and concise representation of the relationship between the quantities being compared.

Conclusion:

The correct answer is option 'A' - 1. The ratio is said to be in its simplest form if the common factor is 1. This ensures that there are no other common factors between the numerator and the denominator, making the ratio as simplified as possible. Simplifying ratios by dividing both the numerator and the denominator by their greatest common factor allows us to obtain a clearer and more concise representation of the comparison being made.