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 go over solving percent problems.
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To solve a problem that involves percents, we want to first translate whatever the sentence is into an equation.
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Whenever you have a number, you are going to write that down in your equation.
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If you have a percent, you need to change it to a decimal.
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You see the word of; that means times; you are going to be multiplying.
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When you see the word what or what number, that means you are going to have a variable.
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That is what you are going to be looking for.
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That is what you are going to be solving for.
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This is almost the same as what we just did the last lesson.
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But now we are going to be looking at variables and solving equations.
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We are going to have to do a little bit deeper into these problems.
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The first set of examples; for example one, 15.
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Remember if we have a number, we are just going to write it straight down into our equation.
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Is; the word is remember means equals; 25 percent; this is write down.
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This we are also going to write straight down.
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But because it is a percent, in our equation, we need to make it into a decimal.
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Percent to decimal, remember we have to move two decimal spaces to the left
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because think of percent as a bigger version of a decimal; decimals are small numbers.
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Whenever you are converting from a percent to a decimal, you have to get smaller.
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The way for you to get smaller is to move the decimal point over to the left.
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The decimal point is over on this side.
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If you don't see a decimal point, it is always at the end of the number.
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We are going to move it one, two spaces.
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The decimal point of 25 percent is going to be 0.25.
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Of course obviously we have to drop the percent sign.
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25 percent is 0.25; that is what I am going to write in my equation.
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0.25; of means times; times what number; this is my variable X.
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Be careful here because whenever you write a dot for times, that looks like the decimal point.
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The best way to represent multiplying is to either write it in parentheses.
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If you are going to show that you are going to be multiplying two numbers, write them in parentheses.
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Or if it is a number with a variable, a letter, then you can just put them together.
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0.25X, that would mean 0.25 times X.
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Here is our equation now; this is what I am solving for.
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15 is 25 percent of what number?--this is the number that I am looking for.
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When I solve for X, remember that since this is 0.25 times X, I need to do the inverse operation.
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0.25 times X, the inverse operation is divide.
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In order to solve for X, I have to divide 0.25.
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0.25 over itself is going to be 1.
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Whatever I do to one side, I have to do to the other side of the equal sign.
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I have to divide this side also by 0.25; this, it looks like a fraction.
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But fractions are division problems; this is the same thing as 15 divided by 0.25.
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Another way to explain why we have to divide, let's say I have 8 equals 4X.
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If I have 4 times a number equals 8, what do I know about X?
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Isn't 4 times 2, 8?--so I know X has to be 2.
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In the same way, I have to solve for X and I can just divide this number by this number.
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Divide this by 4; divide this by 4; 8 divided by 4 is 2.
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That gives me 2 equals X.
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Here 15 divided by 0.25, I need to actually solve that out in order to find X.
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Let's review over how to divide numbers with decimals.
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If I am going to divide these two numbers, remember that the top number is what goes inside when you divide.
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15 on the inside; 0.25 on the outside.
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The decimal point for this number is at the end because we don't see one.
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It is always at the end.
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If I need to add 0s to this number, I can because
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I can always add 0s to the end of a number behind a decimal.
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If it was before the decimal, I can't because then that will just become 150 instead of 15.
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As long as it is behind the decimal and it is at the end of a number,
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you can add as many 0s as you want.
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I can add two 0s; I can add three; I can add ten; however many I need.
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This number, we want to change to a whole number.
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I need to move the decimal point over two spaces to the right to make the decimal point at the end.
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If I move two decimal places for this number, then I have to move this two decimal places over here.
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Then I am going to take that decimal point up.
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25 goes into 15 zero times; 25 goes into 150 how many times?
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Think about quarters; 25 cents or 25 is like a quarter.
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How many of those fit into 100 or a dollar?--four.
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Four quarters is a dollar; think of 150 cents.
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25 cents goes into 150 cents or 1 dollar 50, how many of them?
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That would be six.
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If you want to just check that, this is 12, 13, 14, 15.
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That becomes 0 when you subtract it; I can bring down this 0.
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25 goes into 0 zero times; I have to fill in this space right here.
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That is 0; subtract it; that is nothing.
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I don't have to bring down another 0 because my remainder is 0.
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My answer then, if I do 15 divided by 0.25, is this number up here, 60.
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This number, if there is a 0 in front of the number like that, then that doesn't mean anything either.
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I can just drop the 0; that would just be 60.
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This 0 I cannot drop.
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This 0 has to stay there because if I drop it, my number is going to change to 6.
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We know that 6 is not the same as 60.
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This 0, it is not after the decimal point so we can't drop that 0.
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My answer just becomes 60.
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If you need to review over this, you can either go back to that lesson, dividing decimals.
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Or we are going to do a few more problems that involve dividing decimals.
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The next one, again we are going to change this into an equation.
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1; is is equals; 4 percent.
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4 percent, again we have to change it to a decimal.
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Be careful; 4 percent is not 0.4.
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Again 4 percent to decimal; the decimal point is at the end right here.
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I go one, two; then put the decimal point there.
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I have an empty space that I have to fill.
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I have to fill that with a 0; it is going to be 0.04.
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Again at the end here, one, two, decimal point; 0.04.
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Of means times; blank, that is what we are looking for; that is my variable.
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I am going to put X there.
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Remember if I put number with variable, that means times.
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This represents... I don't have to put a dot here.
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I don't have to use parentheses when it is number with variable.
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Again how do I solve for X?--look at this example again.
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If we are going to do 8 equals 4 times a number, I can take this number, divide it by this number.
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8/4; that is going to give me X.
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Then I have to do this number divided by this number.
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Remember that this over this becomes 1.
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This whole side, my right side, just becomes 1X.
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1X is the same thing as X.
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That is probably a little bit hard to understand, 1X being the same as X.
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But it is like me saying I have an apple.
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If I say I have an apple, you know I only have 1 apple.
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Even though I didn't say I have 1 apple, you just know because how many A's do you see?
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You see one; an A is the same thing as 1A.
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An apple is the same thing as 1 apple.
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Just think of that as having 1X; again we have to divide that; 1.
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Be careful, the top number is going to go inside.
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0.04, the bottom number, is going to go on the outside.
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Again I have to move this decimal point over one, two spaces to the right.
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That means I have to take this decimal point; it is at the end.
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Go one, two spaces; I have to fill these in with 0s.
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There is my new spot for my decimal point; I bring it up.
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4 goes into 10 how many times?--4 times 2 is 8.
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4 times 3 is 12; 12 is too big; it only fits into 10 twice.
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2 times 4 is 8; subtract it; I get 2.
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I am going to bring down this 0.
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4 goes into 20 how many times?--five times.
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4 times 5 is 20; subtract it; I get a remainder of 0.
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I can stop there; my answer becomes 25.
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I don't have to put that decimal because it is a whole number and it is at the end.
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My answer X is 25; right here, this is 25.
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Again 1X is the same thing as X; what did this become?
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This became 25; if 25 is X, then I can just say that X is 25.
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It is the same exact thing.
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The next one, 20 equals 100 percent; to decimal.
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Again start at the end; you are going to go one, two; right there.
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It is going to be after the 1; 1.0.
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Remember if the 0s are at the end of a number behind the decimal point, then I can just drop it.
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Isn't this the same thing as 1?--I can just write 1.
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100 percent as a decimal is 1; times; of means times.
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What number, that is my variable; 1 times X; 20 equals 1X.
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Remember 1X is the same thing as X because if I have 1 apple,
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that is the same thing as just saying I have an apple.
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If you want, you can go ahead and divide the 1 just like we did the other problems.
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20 divided by 1 is 20.
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Whenever you have a number divided by 1, it is always itself.
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20 equals X; or I can flip this around.
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If 20 equals X, then isn't that the same thing as X being 20?
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Either way, that is correct; we just want to know what the number is.
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The number is 20; or you can say 20 is the number.
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It is the same exact thing.
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Let's do a few more examples; these are a little bit different.
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What percent of 50 is 10?
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Now the variable, what we are solving for, is a percent.
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Be careful here; what percent, I am going to make that X.
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Times, times; 50, 50; is, equals; 10, 10; X times 50 equals 10.
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Remember you can change this if you want to 50X just like we did the other problems
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because a number times a variable, you just put it together with the number in front.
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50X equals 10; it is the same thing.
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How do we solve for X then?--how do we get what X is?
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Remember my example?--let's say I have 3 times X equals 6.
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You can do this in your head and know that 3 times 2 equals 6.
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Another way for you to solve it is to do 6 divided by this number; this divided by this.
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Same thing; we can just do 10 divided by 50.
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It is not 50 divided by 10.
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It is this number divided by this number, the one that is multiplied to the variable.
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I can show you this way; 50/50, that is 1.
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10/50, that is what you have to do; 10 divided by 50.
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Again fractions are the same thing as division; 10 divided by 50.
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A shortcut way of doing this is if you are dividing two numbers
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with 0s at the end of it, you can just cross out the 0.
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If there is one 0 up here and one 0 down here, you can just cross out
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one 0 from each of the numbers as long as there is 0s in both numbers.
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But we are just going to go ahead and just divide it this way.
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50 divided by 10; it is not going to go into this number.
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This number is too big to go into this number.
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I am going to have to use my decimal point.
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Do I move it at all?--no, because there is no decimal point here.
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I can just bring it up, bring it straight up.
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I can add 0s at the end behind the decimal at the end of a number.
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Now I can just look at this, 1-0-0, 100.
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50 goes into 100... 50 plus 50 is 100; or 50 times 2 is 100.
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Think of 50 cents; 50 cents goes into 100 cents how many times?
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100 cents is the same thing as a dollar.
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50 cents goes into a dollar twice; this becomes that.
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Subtract it; you get 0; no remainder; that is my answer.
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I don't have to bring down anymore 0s because my remainder became 0.
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When I divided this, my answer became 0.2; X equals 0.2.
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Here is the thing though; they are asking for percent.
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Even though this is my answer, this is my answer as a decimal.
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They want it in percent; they are asking what percent.
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They are not asking what decimal; what percent?
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I have to change this number to a percent; decimal to percent.
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Remember decimal is a small number; percents are larger.
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I have to go from a small to a larger.
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That means I have to move the decimal point over two spaces; but which way?
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If I go to the left, I am going to get smaller.
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But if I go to the right, then I start getting whole numbers.
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I make the number bigger.
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0.2, to make it into a percent, I need to make it bigger.
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I need to go to the right; one, two.
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I have to fill this space with something.
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0.2 as a percent will be 2-0 and then percent.
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The decimal point is right here; it is at the end.
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If it is at the end, remember you can just... it doesn't have to be there.
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You can make it invisible.
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Then we have to write the percent sign because we changed it to a percent.
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My answer is then 20 percent; that is my answer.
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20 percent of 50 is 10.
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Another one; again what percent, make that X, your variable.
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Times 75; is is equals; 7.5.
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Again we have to do this number divided by this number; 7.5 divided by 75.
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Again if you want to see it, I can show you this way.
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because this you have to get rid of by dividing it.
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This 75/75 is 1; X times 1 is just X.
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X equals; then I have to actually divide that to find the answer.
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Here I don't have to move the decimal point anywhere because it is at the end.
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This decimal point will just come straight up.
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75 goes into 75 how many times?--once.
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1 times 75 is 75; subtract it; I get 0.
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I don't have to go any further; 0.1 is my answer; X equals 0.1.
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But again remember it is asking for percent.
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Be careful that you don't forget to change it to a percent.
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I am going to put that here to represent decimal.
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To change it percent, I am going to go one, two, point.
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1; fill this space with a 0; put the percent sign.
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0.1 in decimal becomes 10 percent; X equals 10 percent; there is my answer.
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The last one for this; again what percent X times... of is times... 4 equals 4?
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This one we can just do in our head; what times 4 equals 4?
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Isn't this 1?--1 times 4 equals 4; 4 times 1, it equals itself.
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I don't even have to solve this; I can just make X equal to 1.
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If the problem is fairly easy, you can just do it in your head, then go ahead.
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There is no need for you to do all the work unless your teacher wants you to show the work.
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Then X equals 1; since X equals 1... I didn't mean to box this.
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That is not my final answer so I don't want to box it.
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Since X equals 1, I need to change it to percent.
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How do you change a 1, a whole number, into a percent?
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Again where is the decimal point?--I don't see it.
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If I don't see it, it is invisible, it is at the end like that.
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Go one, two, point here; I have two spaces to fill.
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This becomes 1-0-0 percent; this X equals 100 percent.
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The next example, we are just going to do a few more, just different types though.
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The other examples, they were the same kind, all the problems on that page.
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15 equals what percent, X, times 150; let me rewrite this equation out.
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Since this is 150 times X, let me just write it here.
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15 equals... remember whenever I do a variable times a number,
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I want to write it together but with the number in front; 150X, like that.
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Then to solve for X, remember I have to do this number divided by this number.
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I am going to divide this side by 150.
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Whatever I do to one side, I have to do to the other side.
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That way this becomes 1X or 1 times X; 1X.
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That is the same thing as X.
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15 divided by 150; no decimal point here; I don't have to move it.
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Instead I need to draw that in; bring it up; add 0s.
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150, we know it doesn't go into 15.
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If you want, you can put a 0 up here; if not, then that is fine.
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Just remember that it is now the next three or just these three.
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150 goes into 150 one time; that becomes 150.
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If you subtract it, it becomes 0; I drew an extra 0 there.
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But you don't even have to bring it down because it is just going to be 0s.
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Remember 0s at the end of a number behind the decimal point means nothing.
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0.1 is my answer; X is going to equal 0.1.
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You can also say 0.1 is going to equal 1X or X; same thing.
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But I can switch it like this; it is asking for percent.
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I need to take this decimal point and go one, two; fill in this space.
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It is going to be 1-0 percent; 0.1 is the same thing as 10 percent.
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The next one, 30 percent, this is written out as percent.
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But it still means the same thing as percent like that.
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30 percent, I have to change that to a decimal.
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30 percent becomes... at the end, you go one, two, right there.
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0.30 or 0.3 because remember it is 0s at the end behind the decimal.
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It doesn't mean anything.
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0.3 or 0.30; of, times; 12; it is number times number.
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I can't write it next to each other like how I do numbers with letters.
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I have to put it in parentheses.
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Is is equals; what number, this is my variable.
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All I have to do to figure out what X is is multiply those two numbers.
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0.30, you know what?--we know that the 0 means nothing.
00:27:40.500 --> 00:27:45.600
Let's just make it easier and just not even have that 0.
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One digit number is easier to multiply.
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I am going to put the 12 on the top; 0.3 on the bottom.
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Multiply it; 2 times 3 is 6; 3 times 1 is 3.
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From here, I only have one number behind the decimal point.
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Start at the end; go place the decimal in there.
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What I just did, when you multiply decimals, you have to count...
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This decimal point is at the end, right here.
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You count to see how many numbers are behind the decimal point.
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Here I only have one; then I start at the end.
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I only go one inwards; that is where the decimal place goes.
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X is 3.6; to finish this equation, 3.6 equals X.
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3.6 is the number; or I can say the number is 3.6.
00:28:54.100 --> 00:29:01.200
The next one, 5 percent, change that to a decimal.
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Start here; go one, two; it is point... fill in that space.
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It is 0.05; it is not 0.5; 0.05.
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0.05 times my unknown which is X; X equals 4.
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Again I have to solve for X which means I have to divide.
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4 divided by 0.05; 4 divided by 0.05.
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I have a decimal point here; I have to move it one, two.
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There is my decimal point; I am going to move it one, two.
00:29:48.400 --> 00:29:56.700
Bring it up; fill in these spaces with 0s; 5 goes into 4 zero times.
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5 goes into 40... 5 times we know 8 is 40.
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Write 40 down here; subtract it; 0.
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I am not finished with the number yet because I still have space up here.
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Bring down the 0; 5 goes into 0 zero times.
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That is why for this, I have to keep going.
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Even though this became a 0, I have to bring down the 0 and solve it again
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because there was an empty space before my decimal point.
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In that case, you have to continue.
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If it is after the 0 like in this problem right here... I'm sorry.
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If it is after the decimal point, then I can stop once I get 0 as my remainder.
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But for this, if there is a space here before the decimal point,
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then I have to go again until I fill in those spaces.
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Here this is 80; X is 80; they are not asking for percent.
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5 percent of 80 is 4.
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The last one, 100 percent of 3448 is what number?
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They are asking for 100 percent of this number.
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100 percent is all of it, is the whole thing.
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100 percent of this number is just this number.
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If you want to solve it out how we solved out the rest of them,
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100 percent as a decimal, again move the decimal point over one, two spaces.
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That becomes 1 or 1.0 which is the same thing as 1.
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Times; times 3448; I am going to change this to parentheses.
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3448 equals what number?--X; 1 times this number is just that number.
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I can say 3448 is the number or the number is 3448.
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That is it for this lesson; thank you for watching Educator.com.