Ratio

Ratios tell the proportional quantity of one thing to another. Ratios are often expressed either with a colon – the ratio of kids to adults is 6:1 (read six to one, meaning there are six kids for each 1 adult) – or like a fraction – the ratio of kids to adults is 

61.

It’s important to remember that even though ratios can look like fractions, they are not the same thing. Fractions express a part of a whole. Ratios show proportional quantities. Put another way, fractions relate part to whole. Ratios relate whole quantity to whole quantity.

One great example of this is that ratios can be flipped, but fractions cannot. The fraction 

12is not the same as 

21. But if a student is looking at a ratio, then the positions of the numbers don’t matter, as long as the labels are kept consistent.

In the kids example, it was given that the ratio of kids to adults is 6:1. This could also be stated as: the ratio of adults to kids is 1:6. As long as both the label and the number are flipped, the meaning stays the same.

This also works if when a ratio is expressed like a fraction:

KidsAdults=61 and 

AdultsKids=16.

Now, even though ratios express different meanings than fractions, there are certain properties of fractions that can be used on ratios expressed like fractions. For example, if one takes the ratio 

KidsAdults=61and multiplies both sides by the variable adults, then this leads to the equation Kids = 6 xAdults. So if a student would like to find out the number of kids in a given situation, they can simply multiply the number of adults by 6.

So a student can work with these ratio-fractions as if they’re normal fractions, as long as they keep in mind that they don’t mean the same thing as a normal fraction.

Ratio questions will often ask a student to relate multiple ratios to each either. A student might be given the names of three people, as well as ratios of those individuals’ incomes or heights, for example. They could also be given ratios that ask you to combine information about a larger group, and then information about parts of that larger group. Or they might be given two different versions of the same ratio – simplified and unsimplified – and be asked to calculate one from the other.

For example, here is Question #46 from the April 2021 ACT:

Here the ratios are about advertisement sales. Note that they include the 

14page number at the beginning just to be confusing. The fact that these advertisements are that size does not affect the answer or how a student should approach the question.

Mary sold twice as many advertisements as Carlos. 

Mary\ SalesCarlos\ Sales=21

James sold three times as many advertisements as Mary. 

James\ \ SalesMary\ \ Sales=31

Since Mary made two sales for every sale that Carlos made, that means that James made 6 sales for every sale that Carlos made. One can find this by rearranging the equations from above to look like: Mary Sales = 2  •  Carlos Sales and James Sales = 3  •  Mary Sales.

Therefore James Sales = 3 • (2•Carlos Sales) = 6 Carlos Sales

James sold 6 Carlos Sales worth, Mary Sold 2 Carlos Sales worth, and Carlos sold 1 Carlos Sales worth. Therefore, there were 9 Carlos Sales worth of total sales, and Carlos sold 1 out of the 9. So the answer is F.