Select all ratios equivalent to 18:12. 30:20 72:48 27:18. 30:20 72:48 27:18
The Correct Answer and Explanation is:
The correct options are 30:20, 72:48, and 27:18.
To determine which ratios are equivalent to 18:12, we must first simplify the original ratio to its most basic form. Equivalent ratios all share the same fundamental proportion. The most effective way to find this is by dividing both numbers in the ratio by their greatest common divisor (GCD).
First, let’s simplify the ratio 18:12. We need to find the largest number that divides evenly into both 18 and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12. The greatest common divisor for both numbers is 6. Dividing both parts of the ratio by 6 gives us a simplified ratio.
18 ÷ 6 = 3
12 ÷ 6 = 2
Therefore, the simplest form of the ratio 18:12 is 3:2. Any ratio that is equivalent to 18:12 will also simplify to 3:2.
Now, we will check each of the given options by simplifying them.
For the ratio 30:20, the greatest common divisor of 30 and 20 is 10.
30 ÷ 10 = 3
20 ÷ 10 = 2
This simplifies to 3:2, so it is equivalent.
For the ratio 72:48, the greatest common divisor of 72 and 48 is 24.
72 ÷ 24 = 3
48 ÷ 24 = 2
This also simplifies to 3:2, which means it is equivalent.
Finally, for the ratio 27:18, the greatest common divisor of 27 and 18 is 9.
27 ÷ 9 = 3
18 ÷ 9 = 2
This ratio simplifies to 3:2 as well, confirming it is also equivalent.
Since all three options, 30:20, 72:48, and 27:18, simplify to the same base ratio of 3:2, they are all equivalent to 18:12.
