## Working with Percents Lesson by Mike McGarry
Magoosh Expert

Solutions to the Practice Problems:

1) What is 60% of 60

Let's translate this into a simple equation.

What --> "x" or what we are trying to find.

is --> "="

60% --> 60/100 or .6

of --> " *"

x = .6 * 60

x = 36

So all we did was multiply 0.6*60 and we get 36 as our answer.

2) 52 is 40% of what number?

is --> "="

40% --. 40/100 or .4

of --> " * "

what number --> x

52 = .4 * x

We divide both sides by 0.4 and we get X = 52/0.4 = 130

Let's do a check and make sure we did everything right.

3) 18 is what percent of 45?

Before we do anything math let's do a ball park. We know that half of 45 is 22.5 So without doing any math/computation we know that 50% of 45 is 22.5 so 18 is going to be less than 50>#/p###

is --> " ="

what percent --> x/100

of --> "*"

18 = (x/100) * 45

18/45 = x/100

.4 = x/100

40 = x

So 18 is 40% of 45.

Notice we can simply divide 18 by 45 to get .4

.4 is 40% in decimal form.

4) What is 50% of 128? 

This one you're just dividing 128 by 2.

x = .5 * 128 or 128/2

128/2 = 64

Working with percents. What is 55% of 400? Or 240 is 30% of what number? Now these could be test problems in and of themselves. They certainly would be things you might have to do in the context of a larger problem.

So in this video I will show a few ways to tackle questions such as this. The first really big idea is Percents as Multipliers. The decimal form of percent is called the multiplier for that percent. This is because we can simply multiply by this form to take a percent of the number. So when we're using percents as multipliers, here are the basic things to remember.

Remember that is means equal. Remember that of means multiply. Change any percent to the multiplier form and replace unknowns with a variable. So, for example, what is 80% of 200? The what, the unknown, that will be x. Is, that becomes equal.

80%, that will become the multiplier, .8. And then we'll multiply that of, times 200. So translating that sentence into math, we get (.08) x (200), we multiply out, we get 160. Similarly, 240 is 30% of what number? 240 equals, 30%, is 0.30, times and then what number, x.

So translating to math. Then, of course, we divide. Move the decimal place over and divide out, we get 800. Now the second way to use this is in questions where we have to find the percent. So 56 is what percent of 800?

So here we set things up again. 56 equals x times 800 and we'll have to remember that that x of course is a multiplier. So we divide out, we can cancel the factor of 8, we get 7 over a 100, which is 0.07. That's a multiplier which corresponds to 7%. Finally, percents and fractions.

Use this approach only if the percent is a very easy fraction. For example, one half or one quarter. So, if it's a very easy fraction, then sometimes it's easier to change things to a fraction. So, we get the question, what is 75% of 280? Well, it's much easier just to remember, 75%, that's three quarters.

What's three quarters of 280? Cancel the 4s, we get 3 times 70, which is 210. Here are some practice problems, so pause the video and practice these now. Here are the answers. So in summary, use percents as multipliers, that is their decimal form, and the method for solving the simple percent problems.

Using the same method to find an unknown percentage. So, there the unknown would be the percentage of itself. We'll get a decimal value. We'll have to remember that as the multiplier form, the decimal form of a percent. And then we can use certain fraction shortcuts for percents.