Free Per Cent

Contributor: Mason Smith. Lesson ID: 11141

Ever try to figure out a tip, tax rate, sales tax, sale price, or . . . Percentages are all around us, so we need to know how to figure these things out. Practice with videos, quizzes, and exercises!


Pre-Algebra, Ratios, Rates, Percentages, and Proportions

learning style
personality style
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!


Bobby wants to buy the new Borderlands game for his PS4. It costs $69.99, and he received a frequent buyer rewards coupon for 25 percent off of his next game purchase, which he wants to use. But, there is also state sales tax of 6 percent, that is applied before the coupon.

  • How much does Bobby need to save to buy the game?

In order to figure this out, you need to know what percent means!

The idea behind percent is a ratio out of 100, but with a special catch that doesn't exist in our normal ratios.

If you need a refresher on proporations, check out the Elephango lesson listed under Additional Resources in the right-hand sidebar.

Per centum, or per hundred, or, more commonly, out of one hundred, is the defining characteristic for percent. Take for example the shaded grids below — for each of the grids, what ratio of the grid is shaded (Hint: There are 100 squares)?

grid examples

  x = 50   x = 96  
  100   100  


When the denominator (bottom number of the fraction) is 100, then you can take the numerator (top number of the fraction) and put a % sign behind it; that means out of 100. So take the ratios from the previous two examples and convert them to percentages:

x = 50%

x = 96%


An interesting fact:

  • If you divide the top of the fraction by the bottom, you will get its decimal, which you can easily convert to a percent.
  • If we have 0.25, then we can move the decimal to the right two places to get the percentage value of 25%.
  • Take the two bar graphs above for example. If we think of the entire graph as 100, then when we get our values, we just move the decimal over two places to get the decimal value.

Let's try it with these graphs below.

  • What is the decimal value for each of the three graphs?
  • Now, write the fraction and percent values!

3 grids

Grid 1:

  x =   93   .93   93%


Grid 2:

  x =   18   .18   18%


Grid 3:

  x =   40   .40   40%


Take a moment and think about this: If you want to find out what percentage something is that is not "out of one hundred," how can we do that? This is the basis of percent equations.

We can think of it as creating a proportion out of 100, that would look like this:

  part = percent
  whole 100


This is a super-useful proportion in anything revolving around percentage, because we can take any 3 values and find the fourth. Let's do that now:

Find the part:

What is 50% of 20?

  x = 50
  20 100


Now, we just cross-multiply and find out how large 50% is: 50 x 20 = 100x, which is the same as 1,000 = 100x or x = 10.

Find the percent:

What percent of 60 is 15?

  15 = x
  60 100


60x = 1,500

x = 25, so 25%

Find the whole:

40% of what number is 14?

  14 = 40
  x 100


1,400 = 40x

I recommend watching this clip, Math Antics- What are percentages?, for clarity on what percentages are:


Now watch How to Solve Percent Equations (below) to more deeply understand how to solve percent equations:


Now that you know how to solve for all parts of a percent, continue on to the Got It? section to practice a bit to ensure that it is firmly understood.

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