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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!
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.
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)?
| 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%
Excellent!
An interesting fact:
Let's try it with these graphs below.
Grid 1:
| x | = | 93 | .93 | 93% | |||||
| 100 | |||||||||
Grid 2:
| x | = | 18 | .18 | 18% | |||||
| 100 | |||||||||
Grid 3:
| x | = | 40 | .40 | 40% | |||||
| 100 | |||||||||
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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