3. Ratios: 4 Out of 5 Agree

I'll bet the odds are 3:1 that you are just as confused as I am when to use the term "rate" and when to use the term "ratio".  They seem similar, if not the same.  No matter...the common core will be asking both types of questions, so we must be prepared for both.

Ratios can be described in three basic ways:

"for every x of these, there are y of those", for example, for every 3 girls there are 2 boys.
...or... the ratio of girls to boys is 3:2 (this is the most common description of a ratio)
...or... the ratio of girls to boys is 3/2  (but this is also common...so who knows)

Like rates, a ratio can be described as x:y, or as y:x ...and both are valid.  In the girls-to-boys example, the ratio can be described as 3:2 (ratio of girls to boys), or as 2:3 (boys to girls). Both ways are perfectly valid depending one what you are trying to solve.


SAFETY WARNING:    Many word problems will describe a ratio one way, and then ask you to answer for the opposite.  For example,

"for every 5 boys, there are 3 girls.  What is the ratio of girls to boys."

See what they did here?  They offered a ratio with girls first and boys second....then reversed the order for the ratio answer asking for boys first and girls second to see if you are paying attention.  Although the ratio was first described as 5 boys to 3 girls, the question is asking for a girls-to-boys ratio, which is 3:5.


Ratio Tables
Tables seem to prevalent in many common core studies.  They set up a table of numbers and expect you (or the student) to interpret ratios based ion the table...or perhaps completing the table.  For example:

There are three school classrooms of 6th graders.  They each have the same exact ratio of boys to girls in their class.

What is the ratio of boys to girls in these classrooms?

How many girls are in class #3?

Now think....the problems is asking for the quantity of girls.  You can set the ratios up any way you want.  Since we are solving for girls, let's show the ratios with girls on top:

The ratio of Girls to Boys is 2:3.  Hence, the ratio of Boys-to-Girls is the opposite, or 3:2.

The ratio of girls-to-boys in classroom #3 must be the same ratio as classrooms #1 and #2, which is 2:3.  Another way to think about it is:  "? is to 12 as 2 is to 3."  The two relationships must be the same.  Set up an equation which shows that the two ratios are equal to each other:

Now solve for ?, which yields the answer 8 girls.


This seems pretty straight forward, so let's try a few ratio problems (answers to follow in the next post):

Ratio Q1:  Three boys can eat 2 pizzas.  What is the ratio of boys to pizzas?  What is the ratio of pizzas to boys?

Ratio Q2:  The ratio of pieces of sausage to pieces of pepperoni on these pizzas is  3:1.

For every ____ pieces of pepperoni, there are ____ pieces of sausage.


Ratio Q3:  The three grade 6 classrooms have the same ratio of Boys to Girls.

 What is the ratio of Boys-to-Girls?

How many Girls are in Classroom #2?

How many Boys are in Classroom #3?