To determine the equivalent simplified ratio of [tex]\(3 : 6\)[/tex], follow these steps:
1. Identify the terms of the ratio:
- The original ratio given is [tex]\(3 : 6\)[/tex].
2. Find the greatest common divisor (GCD):
- The GCD of 3 and 6 is the largest number that divides both 3 and 6 without leaving a remainder. In this case, the GCD is 3.
3. Divide both terms of the ratio by the GCD:
- To simplify the ratio, divide each term by 3:
[tex]\[
\frac{3}{3} : \frac{6}{3}
\][/tex]
4. Perform the division:
- Simplifying each term:
[tex]\[
3 \div 3 = 1
\][/tex]
[tex]\[
6 \div 3 = 2
\][/tex]
5. Write the simplified ratio:
- After the division, the simplified ratio is [tex]\(1 : 2\)[/tex].
So, the ratio [tex]\(3 : 6\)[/tex] is equivalent to [tex]\(1 : 2\)[/tex].
