The Correct Answer and Explanation is:
The equivalent ratio for 36:99 in its simplest terms is 4:11.
To find the simplest form of a ratio, we must identify the greatest common divisor (GCD) for both numbers. The GCD is the largest number that can divide both 36 and 99 without leaving a remainder. This process ensures that the proportional relationship between the two numbers is preserved while expressing it with the smallest possible whole numbers.
First, let’s list the factors for each number.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 99 are 1, 3, 9, 11, 33, and 99.
By comparing these two lists, we can see that the common factors are 1, 3, and 9. The largest of these is 9, making it the greatest common divisor.
Next, we divide both parts of the original ratio by this GCD.
For the first number:
36 ÷ 9 = 4
For the second number:
99 ÷ 9 = 11
Therefore, the simplified ratio is 4:11. This ratio is considered to be in its simplest form because the numbers 4 and 11 are coprime, meaning their only common factor is 1. No further simplification is possible. The ratio 4:11 is equivalent to 36:99, as it represents the exact same relationship. For every 4 units of the first quantity, there are 11 units of the second, maintaining the original proportion in its most reduced form.
