There are three basic types of percentage problems:


MISSING PART:
Finding what quantity is a given percentage of another

There are 60 students in the class and 20% play football. How many students play football?


MISSING PERCENT:
Finding what percentage one quantity is of another

There are 60 students in the class and 12 play football. What percentage of the students play football?


MISSING WHOLE:
Finding the whole quantity (ie the 100%), given what percent a certain quantity is.

There are some students in a class and 12 play football. If 20% of the students in the class play football, how many
students are there in the class?


PERCENT WHOLE - The percent whole is ALWAYS 100%.


The relationship between the part and the whole is the same as the relationship of a percent part to 100%.
part_whole_percent_whole.JPG
As you can see in this image, the proportion between the part and the whole is the same as the proportion between the percent part and the percent whole.
part_whole_percent_whole_scribble.JPG

A proportion occurs when two ratios are equal to each other. The proportion below can be stated as: “a is to b as c is to d.”
a_b_c_d.JPG


example_1.JPG

example_2.JPG


example_3.JPG


Try this interactive activity


Now let's look at dual number lines.


Source:

http://www.colin.edu/gedonline/ILP/ILP%202-Solving%20Percent%20Problems.pdf