Final answer:
To determine which ratios form a proportion, set each pair of ratios equal to one another and check if they are true. 1/6 & 3/8 and 2/3 & 8/12 form proportions, while 2/5 & 5/2 and 3/4 & 9/16 do not.
Step-by-step explanation:
A proportion is created when two ratios are found to be equivalent or equal. To determine which ratios form a proportion, we can set each pair of ratios equal to one another and see if they are true.
- 1/6 and 3/8: To check if they form a proportion, we can cross-multiply and see if the products are equal. Cross-multiplying gives us 1 x 8 = 6 x 3, which is true. Therefore, 1/6 and 3/8 form a proportion.
- 2/3 and 8/12: Cross-multiplying gives us 2 x 12 = 3 x 8, which is also true. So, 2/3 and 8/12 form a proportion as well.
- 2/5 and 5/2: Cross-multiplying gives us 2 x 2 = 5 x 5, which is not true. Therefore, 2/5 and 5/2 do not form a proportion.
- 3/4 and 9/16: Cross-multiplying gives us 3 x 16 = 4 x 9, which is true. So, 3/4 and 9/16 form a proportion.