The ratio 75: 125 in its simplest form is Written as:

Options

A. `3:5`
B. `5:3`
C. `2:3`
D. `3:2`

Answer

To simplify the ratio 75:125, we follow these steps:

1. **Identify the Ratio**: We start with the ratio 75:125.

2. **Find the Greatest Common Divisor (GCD)**: We need to find the GCD of 75 and 125. The GCD is the largest number that divides both numbers without leaving a remainder.
- The factors of 75 are: 1, 3, 5, 15, 25, 75
- The factors of 125 are: 1, 5, 25, 125
- The common factors are: 1, 5, 25. The greatest of these is 25.

3. **Divide Both Terms by the GCD**: Now we divide both terms of the ratio by the GCD (25).
- \( 75 ÷ 25 = 3 \)
- \( 125 ÷ 25 = 5 \)

4. **Write the Simplified Ratio**: After dividing, we get the simplified ratio of 3:5.

Thus, the ratio 75:125 in its simplest form is 3:5.