The Correct Answer and Explanation is:
Of course. Here is the correct answer and a detailed explanation.
The correct equivalent ratio in simplest terms is 4 : 11.
To find the simplest form of the ratio 36 : 99, the goal is to reduce both numbers to the smallest possible whole numbers while maintaining the same proportional relationship. This is achieved by finding the greatest common factor (GCF) of both 36 and 99. The GCF is the largest number that divides evenly into both numbers.
First, we can identify the factors for each number in the ratio.
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 the two lists of factors, we can see that the common factors are 1, 3, and 9. The largest of these is 9, which makes 9 the greatest common factor.
The next step is to divide both parts of the original ratio by the GCF, which is 9. This will scale down the numbers to their simplest form.
For the first part of the ratio:
36 ÷ 9 = 4
For the second part of the ratio:
99 ÷ 9 = 11
By replacing the original numbers with these new, simplified numbers, we get the new ratio.
Therefore, the ratio 36 : 99 in its simplest terms is 4 : 11. This is the final answer because the numbers 4 and 11 have no common factors other than 1, meaning the ratio cannot be simplified any further. The relationship of 4 to 11 is proportionally identical to the relationship of 36 to 99.
