WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to be finding percents of a number.
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When we are finding a percent of a number, that means we are finding a portion of a number, some part of a number.
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Whenever we have a percent of a number, let's translate the sentence into an equation.
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Of means times; whenever you see the word of in the sentence, it means times.
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Of like this is times.
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When you see the word what, what means the unknown.
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What is what we are looking for; that is going to be the variable.
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What is the variable.
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Whenever you see the word is, is means equal.
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Whenever you see the word is, you are going to write that symbol.
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Whenever you are finding a percent of a number, you are always going to be
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multiplying the percent with the number because of is times.
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Here what is a variable X; you can use whatever variable you would like.
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You can use A; you can use B; you can use Z; it doesn't matter.
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X is; is means equals; 30 percent.
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30 percent, whenever we solve with percents, we have to change it to a decimal.
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Remember we can't solve with a percent number.
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Remember to change percents into a decimal, you are going to start from the end of the number.
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If you don't see the decimal point, then it always belongs at the end of a number.
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You are going to move two spaces to the left.
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You know it is going to be to the left when you change it to a decimal because decimals are small.
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Think of decimals as smaller than percents.
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To change from a percent to a decimal, we are going to move the decimal point
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over to the left because that is going to make the number smaller.
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Two spaces; it is going to go one, two.
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That is where the decimal point is going to go.
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Here it is going to be 0.30; this is going to change to 0.30.
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Of always means times.
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Here I want to show that I am going to multiply this number to this number.
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Be careful because we don't want to use X for times anymore because here we have X as a variable.
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Instead of using X, use parentheses.
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You also probably know about the dot as times; sometimes that is OK.
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But between two numbers, you don't want to use dot because that looks like a decimal also.
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Maybe if you write it a little bit too low, it might look like a decimal.
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Whenever you are going to multiply two numbers together, it is always best to just use parentheses.
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Writing the number in parentheses like that between two numbers,
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it shows that you are going to be multiplying those two.
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What is 30 percent of 100?
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You know that you are going to be multiplying 0.30 with 100 to find the missing value X.
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100 times 0.30 is going to be 0; then 0; 0; I'm sorry.
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If you want to just multiply this 0 out, you can do that.
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Then multiply this through under; put a 0 here; 3 times 0; 0; 3.
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3; 0; 0; 0; be careful when you have so many 0s.
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Within the problem, because we multiplied, how many numbers are behind the decimal point?
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There is two numbers; one, two; we have two numbers behind the decimal point.
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You are going to go to the answer starting at the end.
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You are going to go one, two.
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That is where the decimal point is going to go; 30.
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X equals... all this was 30; there is a shortcut.
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Whenever you multiply a decimal number, to a multiple of 10... that is 10, 100, 1000, 10000.
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Whenever you have a number multiplied to a number with 1
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and then 0s like 100, there is a shortcut way of doing this.
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You can count how many 0s there are in that number; 100 has two zeros.
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Then you are going to move this decimal point two spaces.
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You know, since you are going to be multiplying, when you multiply, the number tends to get bigger.
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You are going to go two spaces to the right
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because moving the decimal point over to the right makes the number bigger.
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You are going to one, two; that is going to give you 30.
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Remember if you don't see a decimal point, it is always at the end right there.
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If you were multiplying this number by 10, let's say you are multiplying it by 10.
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10 has only one 0.
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You would only move the decimal point over once to the right.
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That would be 3.0 which is the same thing as 3.
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Remember if there is a 0 at the end of a number behind the decimal point, it is as if it is not there.
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3.0 is the same thing as 3.
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If you are multiplying by 1000, 1000 has three 0s.
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You would have to move the decimal point over three spaces.
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Remember if you have an empty space, you have to fill it in with an extra 0.
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That is the shortcut when multiplying by a number that is a multiple of 10; 10, 100, 1000, and so on.
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You just have to count the number of 0s and then move the decimal point over that many spaces.
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What is 30 percent of 100?--that is 30; 30 is 30 percent of 100.
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We are just going to do a few more examples.
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Here 50 percent of 18 is... here 50 percent.
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Again remember whenever we have to solve using percents,
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we have to change it to a decimal because you can't solve with a percent.
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If you have a percent, then you need to change it to a decimal.
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Remember percent to decimal.
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If we have a percent, 50 percent, you want to move the decimal point
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over two spaces between percent to decimal or decimal to percent.
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From percent to decimal, you start at the end right here.
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You have to move two spaces to the left because remember decimals are small numbers.
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You want to turn this number into a smaller number.
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To do that, you have to move the decimal point over to the left.
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If you move it to the right, then the number gets bigger.
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So move it to the side that is going to make it smaller.
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Two spaces, it is going to be right here.
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One, two; drop the percent sign; becomes 0.50.
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Or because this 0 is at the end of a number behind the decimal point, it is as if it is not there.
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You don't even have to write it.
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0.50 is the same thing as 0.5; it is the same thing.
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This is 0.50 or 0.5; of means times.
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Remember if I am going to multiply two numbers together, I want to write it in parentheses.
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Times 18 is; is is equals; then the number X which is what we are solving for.
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As long as you know that you have to multiply the percent with the number,
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because of is between the two numbers, again 50 percent you change to a decimal.
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As long as you know that you have to multiply these two, you don't have to write it into this equation
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because all we are doing is finding percents of a number; of meaning times.
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You just have to be able to multiply these two numbers together.
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The reason why I am saying write an equation is because for the next lesson,
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we are going to have to solve for maybe this number or solve for the percent.
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This number will be given to you.
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In that case, when you are solving for another number,
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this is the easiest way for you to be able to write an equation
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and know what your variable is, what it is you are solving for,
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because a variable is always what you are solving for.
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If you don't want to do it this way, then just make sure you remember to multiply.
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Of means times; you are going to be multiplying the number with the other number.
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0.5 times 18; I am going to write that here; 18 times 0.5.
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8 times 5 is 40; 5 times 1 is 5; plus 4 is 9.
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Within here, how many numbers are behind the decimal point?
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I only have one; starting right here, you are going to go inwards one.
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My answer is going to be 9.0 or 9.
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9.0 and 9 is the same thing.
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Again 0 is at the end of a number behind the decimal point so you can just drop it; 9.
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50 percent of 18 is 9; 50 percent means half.
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50 percent means half; what is half of 18?
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Half of 18 is 9 meaning if you had let's say 18 pieces of candy.
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You had to split it in half; you can only take half of them.
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You take half; your brother or sister has to take the other half.
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Then you would take 9; your brother or sister would take the other 9.
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50 percent means half.
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All you have to do is 50 percent of 18, you just figure out what half of 18 is.
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The next one, here 8 percent; from percent to a decimal.
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Again you are going to start right here.
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You are going to move two spaces to the left.
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You are going to go one and two.
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Point... there is an empty space right here.
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You have to fill it with a 0; 0; 8.
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Then again you are going to drop the percent because it is no longer a percent.
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0.08; 8 percent is 0.08; of means times; 6.
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Again write it in parentheses when you are multiplying two numbers.
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Is equals the number X or blank.
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0.08 times 6; 0.08 times 6; 8 times 6 is 48; this is just 0.
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How many numbers do I have behind the decimal point?
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I only have two; there is none right here.
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Decimal point is at the end right here; I only have two.
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From the end, I am going to go in two spaces; one, two; right there.
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8 percent of 6 is 0.48.
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The next one, 99 percent of 100 is.
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99 percent changes to a decimal because you are solving with it; 99 percent.
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You are going to go one, two; it is going to be 0.99.
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Of means times; 100 in parentheses; equals something; 0.99 times 100.
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Let's do our shortcut; remember if you want, you can multiply it out like this.
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Remember whenever you multiply a number that is a multiple of 10, meaning 10, 100.
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Or I'm sorry; not a multiple of 100; but if you have a power of 100; 10, 100, 1000, and so on.
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What that means is any number with a 1 with a bunch of 0s; 10, 100, 1000, 10000, and so on.
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Since I have 100 and 100 has two 0s, I am going to take the decimal point.
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I am going to move it two spaces.
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But remember I have to move it to the right two spaces
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because when you multiply by 100, that means your number has to get bigger.
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To make this number bigger, I am going to move it to the right.
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One, two; that is where my decimal place is going to go.
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That is going to be 99.0.
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Or remember if it is at the end of a number, you can just drop it.
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You can make it invisible; 99; 99 percent of 100 is 99.
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Whenever you find a percent of 100, it is always just that number.
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If I have 1 percent of 100, that is going to be 1.
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If I have 2 percent of 100, that is going to be 2.
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If I have 100 percent of 100, that is going to be 100.
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Whenever you take a percent of 100, it is just going to be this number without the percent sign.
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68 percent of 100 is 68; that is only if this number is 100.
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Let's just do a few more; what is 25 percent of 60?
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This is what we are solving for; I can make that into my variable.
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Use a question mark; you can do a little blank; is equals.
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25 percent; percent to decimal; I am going to change 25 percent.
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Start right here at the end; you are going to go in one, two.
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It is going to be 0.25; of means times.
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Again since you are multiplying two numbers together,
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you are going to write it in parentheses like that.
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To solve this, I have to... to find the what, to find this, I have to multiply 0.25 with 60.
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60 times 0.25; this is 0; 6 times 5 is 30; put a 0 here.
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2 times 0 is 0; 2 times 6 is 12.
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Add them together; 0; 0; 5; 1.
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How many numbers are behind decimal points?--I only have one, two.
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You are going to start here; you are going to go one, two.
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Remember 0s are at the end of a number behind the decimal point.
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This is just going to be 15; X, this unknown, is 15.
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That means 15 is 25 percent of 60.
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What number is 10 percent of 10?
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Again what number is the same thing as just what or blank or question mark.
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You are looking for the number.
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Is 10 percent; one, two; 0.10; of 10.
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I know that 10 times 10 is 100.
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You can just move the decimal point over that many times.
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Or we can just use our shortcut.
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Since I am multiplying a decimal by 10, how many 0s do I have in 10?
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I only have one 0.
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I am going to move this decimal point over one time.
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It is going to be 1.0; but that is the same thing as 1.
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You can just drop this 0.
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If the decimal place is at the end of a number, then you can just make that invisible.
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You can just write that as 1; that means 1 is 10 percent of 10.
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Find 5 percent of 40; we want to find 5 percent of 40.
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5 percent; this right here is the same thing as this.
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We still have to change this; be careful.
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Just because you don't see the percent sign doesn't mean that you can just drop this number down.
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It is still a percent; you have to change this to a decimal.
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5 percent; again start at the end; you are going to go one, two.
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Going to be point, space right here, 0, 5; of is times; 40.
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You are going to multiply these two numbers together; 0.05 times 40.
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0 times 5 is 0; 0 times 0 is 0; put a 0 down there.
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4 times 5 is 20; 4 times 0 is 0; add the 2.
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Be 0, 0; remember we are adding them down; 200.
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How many numbers total are behind decimal points?--I only have two; these two.
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I am going to go from here; I am going to go one, two; in two spaces.
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My answer is 2.00 which is remember the same thing as just 2.
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My answer is going to be 2; 5 percent of 40 is 2.
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100 percent of 18; 100 percent of 18.
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When I say 100 percent, I am trying to say all of it.
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This is like saying all of 18; 100 percent of 18 is all of 18.
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What is all of 18?
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All of 18, if you have 18 pieces of candy, what is all of it?
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How many would be considered all of it?--18.
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100 percent of 18 is just 18.
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If you want to just solve it out, 100 percent into a decimal is going to be one, two, 1.0.
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Or remember this is the same thing as 1.
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Even though you don't see a decimal here, numbers always have a decimal point.
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It is just if you don't see it, if it is invisible, it is always at the end.
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100 percent is the same thing as 1 in decimal.
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It is like saying 1, or 1.0 if you want, times 18.
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What is 1 times 18?--isn't that 18?
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Again shortcut, if you have 100 percent, you are saying what is all of it?
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All of 18 is 18.
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1 percent of 2000; into a decimal.
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Right here, you are going to go one, two; the decimal point.
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Empty space; you are going to fill it in with a 0; and 1.
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1 percent in decimal is 0.01; be careful that you don't just make it 0.1.
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Of, times; 2000; multiply it out; times 0.01; this is 0; 0; 0; 2.
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Then this is just all 0s so I don't have to write that in.
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It is like adding 0s.
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If I add 0s to this number, it is just going to be that same number.
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From here, how many numbers are behind decimal points?--two.
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Start from here; you are going to go one, two, decimal point.
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My answer here is going to be 20.00.
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Again if the 0s are behind the decimal point at the end of a number, you can just drop them.
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I can drop this, drop this; it will be 20 point.
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But then I can just drop that, make that decimal point invisible if it is at the end.
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It will just be 20.
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The final example, a bag of candy contains 40 pieces.
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If Susanna ate 20 percent of the candy or everything in the bag of candy, how many pieces did she eat?
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A whole bag contains 40 pieces; she ate 20 percent of it.
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How many pieces did she eat?--look at this; 20 percent of the candy.
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What is the candy?--how many pieces does the bag of candy contain?--40 pieces.
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It is like saying she ate 20 percent of the 40 pieces.
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20 percent, again if I want to solve with this number, I have to change it to a decimal.
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20 percent to decimal; I am going to start here; go one, two; is 0.20.
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Of is times; you are going to multiply what?
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The 40 because she ate 20 percent of all the pieces; times 40.
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Here thing is going to be...
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Remember if the 0 is at the end of a number and it is behind the decimal point, I can just drop it.
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This is the same thing as 0.2 times 40.
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I can't drop this 0; be careful here.
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Don't drop the 0 because this 0 is not behind the decimal point.
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Decimal point is right here; right there.
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Since it is not behind the decimal point, I can't drop the 0.
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But this one, I can; that will just make it easier to multiply.
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40 times 0.2 is going to be 80.
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I only have one number behind the decimal point.
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Start here; you are going to go in one space.
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0.2 times 40 is going to be 8.
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Good thing with word problems is that you can estimate if your answer sounds correct.
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Let's say I forget to count how many numbers I have behind decimal points and I just leave it as 80.
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80 can't be my answer because if the bag of candy contains only 40 pieces, Susanna ate 20 percent of it.
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Would it make sense if my answer was 80, that she ate 80 pieces?
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There is only 40 pieces; I know this answer sounds correct.
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It seems correct; it seems reasonable; remember 50 percent is half.
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If Susanna ate 100 percent of the candy, that means she would have eaten all of the candy.
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Then my answer would just be 40.
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If Susanna ate 50 percent of the candy, remember 50 percent is half of the number.
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If this said 50 percent, then you would have to just find half of 40.
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She would have eaten 20 pieces of candy.
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She only ate 20 percent; that means she has to have eaten less than half.
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If 20 is half, we know 8 is reasonable then because it has to be less than half.
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That is it for this lesson; thank you for watching Educator.com.