How did we get the answer? We added up the number of “parts” in the ratio (2 parts boys plus 1 part
girls, or 3 parts all together) and divided it into the total number of students. In other words, we divided
24 by 3. This told us that the class contained 3 equal parts of 8 students each. From the given ratio (2:1),
we knew that two of these parts consisted of boys and one of them consisted of girls.
An easy way to keep track of all this is to use a tool we call the Ratio Box.
Here’s how it works:
Let’s go back to our class containing 24 students, in which the ratio of boys to girls is 2:1. Quickly sketch
a table that has columns and rows, like this:
This is the information you have been given. The ratio is 2:1, so you have 2 parts boys and 1 part girls,
for a total of 3 parts. You also know that the actual number of students in the whole class is 24. You start
by writing these numbers in the proper spaces in your box.
Your goal is to fill in the two empty spaces in the bottom row. To do that, you will multiply each number
in the parts row by the same number. To find that number, look in the last column. What number would
you multiply by 3 to get 24? You should see easily that you would multiply by 8. Therefore, write an 8 in
all three blanks in the Multiply By row. (The spaces in this row will always contain the same number,
although of course it won’t always be an 8.) Here’s what your Ratio Box should look like now:
The next step is to fill in the empty spaces in the bottom row. You do that the same way you did in the last
column, by multiplying. First, multiply the numbers in the boys column (2 × 8 = 16). Then multiply the
numbers in the girls column (1 × 8 = 8).
Here’s what your box should look like now: