Make an equivalent ratio table for each class to represent its solution. Each table should show at least three equivalent ratios. Make sure to indicate which ratio table belongs to which class.

Question

Two sixth grade science classes are making saltwater solutions. The first class (Class A) is using a ratio of three parts salt to five parts water. The other class (Class B) is using a ratio of two parts salt to four parts water. Make an equivalent ratio table for each class to represent its solution. Each table should show at least three equivalent ratios. Make sure to indicate which ratio table belongs to which class.

Answer 1

Hi Caitlin S.,

Sure. Equivalent ratios means ratios that have the same proportions of ingredients. You can make these by multiplying each quantity in the original recipe by the same number value. So for 3 parts salt : 5 parts water, you could also equivalently have: 6 parts salt: 10 parts water, or 9 parts salt : 15 parts water, for example. You can also divide by the same value (since multiplying by a number is the same as dividing by the reciprocal of that number), so also: 1 part salt : (5/3) parts water. The multiple doesn't have to be an integer, it just has to be a real number. Usually, it only makes sense to use a positive real number; you can't for example add -3 parts of salt to -5 parts of water to make a solution!

Possibly this problem is hoping that you'll include a line on each equivalent table that has the same particular value of salt (such as 6), or the same particular value of water (such as 20), representing the least common multiples of the respective class recipe amounts?

If you want to wow your teacher, you might point out the salt, if it is sodium chloride, is only soluble at 26% (w/w final solution), so both classes' mixtures are saturated (ratio 26:74), and have undissolved salt present. Such solutions can be useful when used in a chamber intended to provide a constant level of relative humidity; different salts used will provide different relative humidity levels. Another reason to use a salt-saturated solution would be to gradually draw moisture from a biological specimen, although solvents such as ethanol are more usually used for that purpose.

-- Cheers, -- Mr. d.