How do you write a ratio in lowest terms

Solution:
1. Given a ratio in the form a : b, where a and b are integers.

2. Find the greatest common divisor (GCD) of a and b. Use the Euclidean algorithm if necessary:
- Divide a by b to get the remainder r.
- Replace a by b and b by r.
- Repeat the process until r = 0.
- The non-zero remainder just before r = 0 is the GCD of a and b.

3. Divide both a and b by their GCD to simplify the ratio:
- Simplified ratio: \frac{a}{\text{GCD}} : \frac{b}{\text{GCD}}.

Example:
- If the initial ratio is 24 : 36, we find the GCD of 24 and 36.
- 36 \div 24 = 1 with remainder 12.
- 24 \div 12 = 2 with remainder 0.
- The GCD of 24 and 36 is 12.
- Simplify the ratio by dividing both terms by 12:
- \frac{24}{12} : \frac{36}{12} = 2 : 3.

Thus, the simplified ratio is 2 : 3.