to simplify the ratio of 50 and 130.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the numbers for which the ratio needs to be simplified.
The problem asks to simplify the ratio of 50 and 130.
Step 2: Write the ratio in its initial form.
$$ 50:130 $$
Step 3: Find the greatest common divisor (GCD) of 50 and 130.
The factors of 50 are 1, 2, 5, 10, 25, 50.
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130.
The greatest common divisor of 50 and 130 is 10.
Step 4: Divide both parts of the ratio by their GCD to simplify.
$$ \frac{50}{10} : \frac{130}{10} $$
$$ 5 : 13 $$
The simplified ratio is $5:13$.
The final answer is $\boxed{5:13}$.
