In this lesson, we're going to talk about percent proportions. In a percent proportion... The ratio between the part and the whole is equivalent to the ratio between the percent and 100. So therefore, you can set it up as an equation or proportion.
So here's the equation that we're going to use. The part divided by the whole is equal to the percent divided by 100. So let's work on some problems using this equation. In the first case, the first type of question we're going to solve is finding the percent. So here's the first one.
20 is what percent of 45? Feel free to pause the video if you want to try it. So we have part.
Divided by whole is equal to percent over 100. I probably should have moved this equation in the middle. Now there's something I want to add to this equation, so this will help you in the future. The part is associated with the word is, or the number that's associated with the word is.
And the whole is the number that is associated with the word of. I think that's going to help a lot. So you need to... recognize that 20 is the part 45 is the whole and we're looking for the percentage so P is 20 W is 45 the percent since that's what we're looking for let's call So now we need to do is cross multiply. 45 times x is simply 45x.
And then we have 20 times 100, which I'm going to leave it like this. Now 45. Let's divide both sides by 45. So, X is going to be 20 times 100, which is 2,000. And 2,000 divided by 45 is about 44.4. So, that's the answer. 20 is 44.4% of 45. Here's another similar example.
What percent of 12 is 27? Feel free to try that problem. So we're going to use the same equation.
Part divided by whole is equal to percent divided by 100. The percent, we're going to make it x. Now what is the part and what is the whole in this problem? The number that is associated with is is the part.
So 27 is the part. The number that is associated with the word of is the whole. So 12 is the whole. So what percent of 12 is 27? Whenever the part exceeds the whole, your percentage is going to be greater than 100. Let's go ahead and find the value of x.
So what we have is 12x, after cross multiplying, is equal to 27 times 100, which is... 2700 now we need to do is divide both sides by 12 and then this is going to give us the answer to 2700 divided by 12 is 225 so 1227 is 225 percent of 12 And so that's how you could read the sentence if you want to. But that's the answer. Now the second thing that we need to talk about is how to find the part.
This question is going to illustrate it. What is 32% of 86? So let's write the equation first. We have the percentage, 32%. Now the number that's associated with the word of is 86, and that's the whole.
So we're looking for the part which we can replace it with x. And now we've just got to cross multiply. So x times 100 is 100x. And 86 times 32, let's find the value for that.
That's going to be 2752. So all we got to do is divide 2752 by 100 and that's equal to 27.52. So 27.52 is 32% of 86 and that's the answer. Here's another example.
What number is 21% of 250? So we're looking for the part once again. Let's replace p with x. The whole is the number associated with the word of, that's 250. We have the percentage, which is 21%, and let's cross multiply.
So once again, we're going to have 100x is equal to 250 times 21. 250 times 21 is 5250. Now let's divide both sides by 100. 52.50 divided by 100 is 52.5. So 52.5 is 21% of 250. By the way, 50 is 20% of 250. 20% is 1 5th. The last thing that we need to cover is finding the base. So here's a problem that will illustrate this example.
30 is 45% of what number? So go ahead and pause the video and you can try this if you want to. So let's start with the equation part divided by whole is equal to the percentage divided by 100. So in this problem, what is the part and what is the whole? Thirty is the part associated with the word is.
We're looking for the whole, which is also known as the base. We're looking for the number that's associated with of. So 30 is P, the whole or the base is X, the percentage is 45. So let's cross multiply. 30 times 100 is 3000, X times 45 is 45X.
So let's divide both sides by 45. 3000 divided by 45 is 66.7. So that's basically the value of x. So that's the base.
So 30 is 45% of 66.7. Here's another example. 22. is 34 percent of what number? So in this example, we can see that the part is 22, and we have the percentage, which is 34. We need to find the whole, or the base.
22 times 100 is 2200, and x times 100 is 2200. times 34 is 34x. So let's find the value of x by dividing both sides by 34. 2200 divided by 34, that's 64.7 if you round it. So 22 is 34% of 64.7. And so now you know how to use the percent proportion formula in order to find the part, the percent or the base which is also known as the whole. Now I want to show you one of my algebra courses that might be useful to you if you ever need it.
So go to udemy.com. Now in the search box, just type in algebra. And it should come up.
So it's the one with the image with the black background. So if you select that option, and if you decide to go to course content, you can see what's in this particular course. So the first section, basic arithmetic, for those of you who want to focus on addition, subtraction, multiplication, and division. And it has a video quiz at the end. It's a multiple choice video quiz.
You can pause it, work on the problems, and see the solutions. It covers long division, multiplying two large numbers, and things like that. The next tutorial is on fractions.
Adding, subtracting fractions, multiplying, dividing fractions, converting fractions into decimals, and so forth. So, you can also... Also take a look at that.
Next, solve the linear equations, which we covered, and just more examples if you need more help with that. The next topic, order of operations, which is also useful. Graph and linear equations.
You need to know how to calculate the slope. You need to be familiar with the slope intercept forms. standard form and just how to tell if lines are parallel perpendicular and so forth and as a quiz that goes with that as well the next topic is on inequalities and absolute value expressions which are also seen in a typical algebra course and then we have polynomials and that's a long section and then factoring you just that's another topic you need to master And then system of equations.
You can solve it by elimination, substitution. There's also word problems as well. Sometimes you've got to solve equations with three variables, x, y, and z. So that could be helpful. Next, quadratic equations, how to use them.
quadratic formula, how to graph them, how to convert between standard and vertex form, and then you have rational expressions and radical expressions, solving radical equations, simplifying it, things like that. And every section has a quiz, so you can always review what you've learned if you have a test the next day. So here we have complex imaginary numbers.
You need to know how to simplify those. Exponential, functions, logs. I have a lot of videos on logs. And then this is just functions in general. Vertical line tests, horizontal line tests, how to tell if a function is even or odd.
And then conic sections. Graph in circles, hyperbolas, ellipses, parabolas. and things like that.
There's two video quizzes because it's actually a long section. And finally, arithmetic and geometric sequences, and series. So, that's my algebra course if you want to take a look at it, and let me know what you think.