Final answer:
A proportion is an equation showing that two ratios are equivalent. For each set of numbers given, a true proportion can be written, but no additional unique proportions can be created without repeating the same ratios.
Step-by-step explanation:
To create a proportion, we must find two ratios that are equal when one ratio from each set of numbers is compared. Here are the answers for each set of numbers provided:
- Using the numbers 2, 5, 20, and 8, a true proportion can be written as 2/5 = 8/20. We cannot create another proportion using the same set without repeating a ratio.
- For the numbers 18, 4, 24, and 3, a true proportion is 18/24 = 3/4. Another proportion using the same set would just be a reordering of the same ratios, so it's not considered different.
- The numbers 4.5, 6, 9, and 12 can form the proportion 4.5/6 = 9/12, and no other true proportion can be formed without repeating ratios.
- Lastly, for the numbers 1/7, 0.2, 5/7, and 1, a proportion can be written as 1/7 / (5/7) = 0.2/1. Another proportion from the same set cannot be made without reusing ratios.
Proportions are equations that show that two ratios are equivalent. A proportion problem can typically be identified when two ratios are compared to establish if they have the same relationship or value. The key to solving proportion problems is finding pairs of numbers that when placed in ratio form, the cross-multiplication yields an equivalent product.