Working with Percents

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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 a 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 equals.

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 0.8, and then we'll multiply that of times 200. So translating that sentence into math, we get 0.80 times 200, we multiply out, we get 160.

Similarly 240 is 30% of what number? 240 equals 0.3, 30% is 0.3 times and then what number, x? So translating to math and 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. We'll have to remember that x, of course, is a multiplier, so we divide out. We can cancel the factor of eight, we get 7 over 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 1/2 or 1/4. 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 3/4. What's 3/4 of 280? Cancel the 4's we get 3x70, which is 210. Here's 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 the unknown would be the percentage of itself, will get a decimal value, we'll have to remember that is the multiplier form, the decimal form of a percent. And then we can use certain fraction shortcuts for percents

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