Math Videos: How To Learn Basic Arithmetic Fast - Online Tutorial Lessons

In this video we are going to focus only on some

basic

math

ematics topics. This is for those of you who really want to improve your

math

skills, so let's talk about how to add and subtract, especially when there are negative numbers. multiply do mental calculations in your head we are going to review the multiplication tables, the ones you should know, we are also going to talk about how to divide and how to convert fractions into decimals, how to add subtract fractions, multiply divide how to convert them to mixed numbers we are going to talk about how to do percentages in your head and how to simplify fractions mentally we are also going to review exponents and even exponential fractions order of operations that we are going to talk about square roots how to simplify radicals cubic roots we are going to get into scientific notation how to convert it to decimal or standard form and vice versa how to multiply divide two numbers in scientific notation even how to take a square root of a number in scientific notation now we are also going to talk about how to solve equations, both linear equations, equations with decimals, fractions, equations involving radicals, cube roots and also how to factor and use the quadratic equation and after that we're going to talk about how to graph linear and quadratic equations and we'll go over some general principal functions and how to do some transformations, so just some of the common topics that you'll see in algebra, but the part The beginning of this video focuses more primarily on

arithmetic

and then for those of you who are looking to do well in algebra, the rest of the video might be helpful to you so let's start with some

basic

addition problems if you want to add 5 plus four, right?

Which is the answer? Now, for those of you who know you know it's nine, but let's say if you don't know the answer to that problem, what you could do is imagine a number line here, you have 0 on the left side negative 1 negative 2 negative 3. and so on to the right you have 1 2 3 4 and five but now let's start from five let's say zero is here and this is five starting from five you want to add four if you want to add you need to go to the right If you want to subtract you have to move to the side left, so since you want to add 4, let's add, we're going to go four units from the right, so 1 2 3 4 and we'll stop here. so this is going to be six seven eight nine therefore five plus four is nine let's try with other examples so what is seven minus three seven minus three is four but we are going to show it with the number line so let's say that this is zero and seven It's somewhere Around here, if we start from seven and we want to subtract it by three, we need to go three spaces to the left, so one two three, so this is going to be six five four, so seven minus three is four, so what?

What about this five minus? Eight, what is the answer to that particular problem? Now five minus eight is negative three, so we're going to start with five, and since we're subtracting, we're going to go eight spaces to the left, so one, two, three, four, this would be five. six seven eight so this is four three two one zero minus one minus two minus three which is negative four plus five minus four plus five is positive one so if you start from minus four and since we're adding, we add five plus four Let's go five units to the right, so one two three four five minus three minus two minus one zero one now you can also add it backwards minus four plus five is the same as five minus four, you can reverse the numbers this will also give you one, so If you started at five and went four units to the left one two three four you would end up in the same place, which is one, so try this one minus eight plus three, by the way, feel free of these problems. to pause the video try it yourself and see if you can get the answer minus eight plus three is minus five so starting at minus eight we're adding three so we're going to go three spaces to the right one two three so minus seven minus six minus five and there it is, what about negative nine minus four?

What is the answer to that problem? So negative 9 minus 4 is negative 13. So if we start at negative 9, we're going to subtract 4, so we need to go four units to the left, so one, two, three, four, this will be negative 10, negative 11 , negative, 12, negative, 13. Now, what if there are three negative signs, like minus 10 minus minus four? Sometimes you can see this in parentheses, but it's the same thing. as if now it was also written like this, whenever you see two negative signs next to each other without any number between them, you can change them to positive, so this is the same as negative ten plus four, a negative multiplied by a negative is positive. um a negative multiplied by a positive is negative and a positive multiplied by a positive is just a positive number, so we have negative 10 plus four, so starting from negative 10 we're going to add four ones or go four ones to the right, like this that one two three four minus nine minus eight minus seven minus six therefore negative ten plus four equals negative six so what happens to eight minus minus three?

How would you make that one so we can change the two negative signs to a plus, so this is a plus three? since we know it's eleven, if we start from eight and go three units to the right, we would end up at eleven, so now let's do a test, let's try these problems eight plus seven, five plus nine, six plus seven and five plus twelve, so try these four problems first. you can use the number line technique and then I'm going to pause the video to take a minute to do that and I'm just going to give you the answers, so 8 plus 7 is 15.

So if you start from 8 and go seven units to the right you should end up with fifteen six plus seven is thirteen five plus nine is fourteen and five plus twelve is seventeen try this let's say if you have nine minus four and uh 12 minus 5 and 14 minus 6 and one plus that's similar to this type of problem 22 minus 13. So in these four problems notice that the positive number is greater than a negative number, when that happens usually your result will be positive so nine minus four equals positive five using a number line if you start at nine and you go four units to the left since you are subtracting four, this will be eight seven six five, so fourteen minus six, if you don't see it correctly, it will look like this: 14 minus 6 is positive 8 and 12 minus 5 that is positive 7 and 22 minus 13 is positive 9.

So you can use the number line to check your answers or if you have a calculator, you can use that too, but it's always good to do mental calculations, try these four. problems seven minus nine four minus twelve five minus sixteen and eight minus nineteen, so notice that the negative number is greater this time, so the result must be negative seven minus nine is negative two, so if you start from seven and travel nine units to the left this will be six five what else let's count it one two three four five six seven eight nine so this would be six five four three two one zero negative 1 negative 2 then we get the answer 5 minus negative 16 you should get negative 11 4 minus 12 is negative 8 and 8 minus 19 is also negative 11, so let's use the number line for one more example.

Now let's use it for four minus twelve, but counting twelve spaces backward might seem like a long task, although you could do it. but we can also write it as negative 12 plus 4, which is the same as 4 minus 12. So if we start at negative 12 and go 4 units to the right, it will be 1 2 3 4. So this is negative. 11 negative 10 negative 9 negative 8. but if you want to take it the long way you can start with 4 and go 12 spaces back 1 2 3 4 5 6 7 8 9 10 11 12. and as you can see you are going to get to minus 8. try these examples minus six plus nine minus 5 plus 14 minus 8 plus 12 and minus 9 plus seventeen so we have a positive number and a negative number.

Notice that the positive number is greater, so when we add these two values ​​we should get a positive value at the end, so negative six plus nine is plus three using a number line if we start with negative six and if we go nine spaces to the right one two three four five six seven eight nine this will be negative five minus four minus three minus two minus one zero one two three minus eight plus twelve that will be equal to plus four minus five plus fourteen that's nine and uh minus nine plus seventeen will give you eight so here's the next round of questions minus 5 plus 2 minus 12 plus 5 minus 16 plus 7 and minus 14 minus five so try them out so starting with minus five we're going to add two ones so one two we're going to go two units to the right, this will be negative four and negative three, so negative five.

Plus two is negative three, so notice that the first number, negative one, is larger, so the result will be negative minus 12 plus five equals negative seven minus 16 plus seven um, you should get negative nine and minus fourteen minus five is negative nineteen try this and if so let's say if we have two negative signs minus three minus five what do you think the answer to that particular problem will be then minus three minus five is minus eight so if we do the number line starting at negative three We're going to subtract it by five, so we have to go five units to the left one two three four five, so this is going to be negative four minus five minus six minus seven and negative eight, so when you have two numbers like two negative numbers written the way we have it in this video, what you could do is simply add three plus five, which is eight, and then make a negative, so eight minus four is the same as eight plus 4 with a negative on the outside, so what could you do?

What we do is say that plus 4 is 12 and add the negative sign to confirm it. We're going to start at minus 8, which is here, and we're going to subtract it by four or go four units to the left, one, two, three, four. so this is negative nine minus ten minus eleven minus twelve so minus seven minus six is ​​the same as 7 plus 6 with a negative on the outside 7 plus 6 is 13 so this is minus 13. and this is going to be negative and then 9 plus 8. so 9 plus 8 is 17, so this will be minus 17. try these negative 8 minus 3 negative nine minus minus fifteen negative twelve minus minus four and minus fourteen minus sixteen, so when you see two negative signs like the one in the right next to each other, you can turn it into a positive number, so it's the same as negative eight plus three, so using the number line, if we start at negative eight, we're going to add three units to the right, one, two, three, so this is going to be negative seven minus six and negative five, so negative nine minus minus fifteen is the same as negative nine plus 15. and negative 9 plus 15 is the same as 15 minus 9, so which you will get plus six so you can reverse it.

If you want, negative 12 minus minus four is the same, I mean, minus minus four is the same as plus four and minus twelve plus four is the same as four minus twelve and that should give you minus eight here we have minus 14 minus minus 16. so that's negative 14 plus 16 and negative 14 plus 16 is the same as 16 minus 14 which is equal to 2. so keep in mind that you can always reverse the order if you have negative 3 plus 8, you can change it, 8 is positive 3 is negative so this is the same as positive 8 minus 3 which is just 8 minus 3 and that is equal to 5. so if you have negative 10 plus 7 you can invert and say that you know what seven minus ten is and the number negative is bigger so when I subtract them I get three but since the sign of the largest is negative this will be negative here the sign of the largest is positive so this is positive so it covers some basic addition , but let's say if you want to add larger numbers, let's say if you want to add 26 plus 74, what would you do without a calculator?

Well, you can write it like this. 6 plus 4 is 10, so we're going to put the 0 here, but let's go to 1. to put it in the next column and then we add one plus two plus seven one plus two is three three plus seven is ten so 26 plus seventy-four is therefore a hundred try with this sum 35 and 62. so 35 plus 62 5 plus 2 is 7 3 plus 6 is 9, so this is equal to 97. Now, what about 47 plus 65, so 47 plus 65 5 plus 7 is 12. You have to transfer the one and then one plus four is five five plus six is ​​eleven, so this gives you are a twelfth now, what about the subtraction?

So let's say if we want to subtract 87 minus 23, let's write it like this 87 minus 23, so 7 minus 3 is 4 and then 8 minus two is six, so this is equal to 64. Not bad, right? So you can see it here eight minus two six and then seven minus three is four, so you get 64. What about this 64 minus 39? So if we subtract 4 minus 9, we'll get a negative number, so I don't really want that, let me put some space between these two numbers. Now, what you could do is borrow a 1 from the 6 so that the 6 becomes a 5. And we're going to put the 1 here, so 14 minus 9 is 5 and then you could subtract 5 and 3, which would give you gives 2.

So 64 minus 39 is 25. Let's try another one like that, so 76 minus 48, so 6 minus 8, that's going to give us a negative number, so let's remove or borrow one. from seven, that becomes a six, so instead of having six we now have sixteen, so sixteen minus eight is eight and six minus four is 2, so we get28. Now what about 125 minus 69, what does it equal? So borrow one from two, so now we have fifteen fifteen minus nine is six and this is nine one and now what we have here is 11 minus six is ​​five, so 125 minus 69 equals 56. try this 42 minus 68 Note that 68 is a number greater than 42, therefore the overall result was negative.

Now you don't want to subtract it as written. What you could do is if subtracting by a larger negative value, invert 68 minus 42, so 8 minus 2 will be six and six minus four is two, since you invert it, add the negative sign, so 42 minus 68 equals to minus 26. Let's try another example: twenty. five minus seventy four, so we subtract twenty five times a larger negative number, so let's reverse it, so four minus five we can't do that, we need to borrow one so that the seven becomes a six and the four becomes fourteen . so fourteen minus 5 is 9 and 6 minus 2 is 4 so we get 49 but we're going to add a negative sign so this is negative 49. so now let's review multiplication, the first thing we're going to do is build a simple multiplication table, so let's start now.

If you can build a table yourself, it will help you know your multiplication numbers. I recommend you do it too because you will see a pattern, for example, what does five look like? multiplied by four now some of you may know the answer but if you are not sure what it is it might be helpful to get a calculator or build multiplication tables and want to know your multiplication numbers up to 12. It will help you with many

arithmetic

calculations that we will do from now on, so don't skip this step now. It may not go up to 12 in this particular example, but I want you to.

I want to give you an idea of ​​how to build a table, so what we are going to do is put numbers in the first row, this will be 1 2 3 4 5 6 7 8 9. and here we will have one two three four five six seven I guess we will go up to eight here and maybe we can get to ten so one times one is one one times two is two and then these numbers will increase by one now two times one is uh two two times two is four two times three is six and these numbers they will continue to increase by two, so look at the pattern and now for the three three times one is three three times two is six three times three is nine three times four is twelve three times five is fifteen three times six is ​​eighteen three times seven is twenty-one three times eight is twenty-four three times nine is twenty-seven three times ten is thirty so notice that now we are just adding three four times one is four four times two is eight four times three is twelve four times four is sixteen four times five is twenty-four times six is ​​twenty-four times 7 is 28 4 times 8 is 32 4 times 9 is 36 and 40 and 4 times 10 is 40. now 5 and 1 is 5. 5 times 2 is 10 and then these numbers will continue to increase by 5. so five times five is twenty-five times eight is forty-five times ten is fifty so these numbers will continue to add up times six six times four is twenty-four six times seven is forty-two and so on seven times one is seven seven times three is twenty-one seven times six is ​​forty-two seven times eight fifty-six and now for the eights, this will continue to increase by eight, so let's say if you wanted to multiply six by eight, then you would search and go to the sixth row and stop once you You get to column eight, so six times eight is forty-eight, so now let's say if you want to multiply seven times nine, here's seven. nine, so from the seventh row we go to the ninth column and we get sixty-three, therefore seven times nine is sixty-three, so let's say if we want to multiply four by six, then the fourth row, six columns, four times 6 is 24.

So that's how you would use it, so feel free to take a moment and study the table and even get to a point where you can construct the table. yourself, go up to 12. you want to know your multiplication numbers, 1 to 12. and then I'm going to ask you about this, so let's say if you want to multiply 5 by 6, this can be written like this or it can be written as five by six five times six is ​​thirty. Now, if you ever forget your board, what could you do? it's um you can add five six times because that's what multiplication is five times six means you're adding five six times and this will give you thirty so for example four times three equals twelve four times three means that you are adding four three times and that is equal to twelve, it can also mean that you are adding three four times, which will also be equivalent to twelve, so five times three according to the table is fifteen, but if you want to convert it to a sum five times three is five. plus five plus five three times or it's adding three five times and that gives you fifteen in both cases, so what is six times four six times four is twenty-four?

If you add six four times you get twenty-four, so at this point make sure you have memorized the multiplication table and then once you do, try this 8 times 7 quiz, just make sure you know it's 56, 9 times 9 is 81 , 7 times 6 is 42, 10 times 5 is 50. Okay, try this, feel free to pause the video to make it twelve. times twelve eight times six four times nine and three times twelve then twelve times twelve is one forty-four eight times six is ​​forty-eight four times nine is thirty-six and three times twelve also thirty-six so 12 times 5 is equal to 60 7 times 9 is 63 8 times 12 is 96 and 11 times 11 is 121.

Okay, let's try some more problems, so what is 12 times 9, 5 times 8 five times eleven, seven times times twelve, twelve multiplied by eleven and finally nine multiplied by eight? So twelve multiplied by nine is 108 5 times 8 is 40 5 times 11 is 55 7 times 12 is 84 12 times 11 is 132 9 times 8 is 72 so make sure you can do such multiplication now, let's say if you have larger numbers Let's say if you wanted to multiply 15 by 8, how would you do it right? You could do it the old fashioned way 15 times 8. eight times five, we know it's forty, so we're going to put in the zero and move the four up and then we're going to multiply eight times one, eight times one, it's eight, but we need add the four, so this equals one twenty.

Now, if you have a calculator with you or can go

online

and type calculations

online

into Google, you can enter this. The number on your calculator 15 times 8 is 120. Now, another way to do this is to divide the 15 um into 10 plus 5. 10 plus 5 is 15 and then multiply by 8. 8 times 10 is 80 and five times eight. is forty now eight plus four is twelve if you add zero you get one twenty so eighty plus forty is one twenty let's try another problem so what is 20 times 14? How would you multiply those two numbers so that 4 times zero is zero and then four times two is eight now we're going to add a zero, so one times zero is zero and one times two is two, so if we add these numbers zero plus zero is zero zero and eight, that's eight and we drop the two we get two eighties, so another The way to multiply twenty by fourteen is an image that you have in mind if you have fourteen twenty dollar bills, what is the value of fourteen twenty dollar bills? twenty dollars?

You know that five twenty dollar bills are a hundred, so another five of another five twenty dollar bills are another hundred and then If you have four twenty dollar bills left over, four twenties are eighty, so if you add this up you have two hundred and eighty dollars and as you can see, you have fourteen twenties on this side, five plus five plus four, that's fourteen. When it comes to money, it's very easy. To do math, everyone understands it now. Another way you could have done this is to separate the 14 into 10 plus 4 and 20 times 10 is 200 if you have 10 20 dollar bills that's 200 and 20 times 4 well 2 times 4 is 8. if you add the 0 you get 80 and then this adds up to 280.

So let's say if you want to multiply point 25 by 15, what would you get? So 5 times 5 is 25, so we'll put the five here and add up. two up five times two is ten plus two, that's twelve, so we need to add a zero five times one is five and five times two, I mean, one times two, that's two, so if we add this we get five, seven and three now. Notice that we have two spaces um after the decimal, so we need two spaces here after the decimal, so this is three point seven five, this is how you can multiply a number in the decimal.

Another way to multiply 15 by 25 is that we know that 0.25 is 25 cents, imagine if you have 15 quarters, 15 quarters have a value of 375 for every four quarters you have as a dollar, so four times 25 cents is one dollar, another four quarters are one dollar and another set of four quarters is a dollar, so there are 12 quarters. we have so far and then 15 quarters we need three more, so the remaining three quarters are 25 cents, that is 75 cents, so you have seventy-five cents, yes, if you add these numbers, if you have them, you have a total of fifteen quarters and four. plus four plus four plus three is fifteen, so let's say if you want to multiply 8 times 17, try this problem but using both techniques, let's do it this way 17 times 8, so 8 times 7, that's 56, let's move the 5 here and 8 times 1 is 8 plus 5, that's 13.

So now let's use the other technique, let's replace 17 with 10 plus 7. So eight times ten is eighty-eight times seven is fifty-six if you add these two numbers eighty and fifty-six six plus zero is six eight plus five is thirteen, you get the same answer 136, so there are many techniques you can use to do mental calculations or even just calculations on paper without using a calculator, but now let's go over some other concepts. Let's say if you want to multiply ten by ten now by instinct, you probably know that this is a hundred, but the way you have to do it is in your mind, you have to multiply one by one, which gives you one and then add the two zeros for example. ten times one well, if we multiply one and one we get one and then we add the three zeros that we see, we have one two three zeros so one that means zero zero zero so that's a thousand so one hundred times one hundred so one times one is one and then we add the four zeros to get ten thousand, so what do you think one hundred times ten thousand is?

Well, here we have a total of six zeros, so this is a million. Okay, so now let's try this principle. For other more difficult problems, let's say if you want to multiply 50 by 100, basically, if you have 50 100 dollar bills, how much money do you have? If we multiply the outside numbers five and one, five by one, it is five and then we add the three zeros, this is five thousand, if you want to multiply 40 by 200, what you must do first is multiply four by two and that will give you eight and then you add the three zeros, so forty times two hundred is eight thousand, so what is thirty times? six hundred, well three times six is ​​eighteen and if we add the three zeros it's eighteen thousand, so how about seventy times eight hundred seven times eight is 56 three zeros, that's 56,000.

Okay, let's try a quiz, try these problems so that these Big calculations that you can do without the use of a calculator, so 40 by 900 looks like you're multiplying very, very large numbers, but remember that all you need to do is multiplying the numbers outside 4 by 9 is 36 and then adding the three zeros. So 40 times 900 is 36,000. So what is 500 times 700? So 5 times seven is 35 and then we have four zeros to add, so this will be 350,000. 60 times 40. So 6 times 4 is four, add the zeros. this is twenty-four hundred, which is eight times five, eight times five, is forty, then add the remaining six zeros, so this equals 40 million.

Now, what is 12,000 times 70,000? That's why you want to know the multiplication tables up to 12. 12 multiplied by 7 is 84 and we have three zeros on this side and four zeros here, so we have a total of seven zeros, so let me make sure I put the comma in the right place, so I need a comma here and here, so this twelve thousand times. seventy thousand is eight hundred and forty million, so regardless of how big these numbers are, as long as you follow the basic principles, you can do calculations up to any limit, by the way, the video you are currently watching is a preview version of a hour. of a longer four hour paid video, so I'll post a link here in case you want to watch the remaining three hours of this video, if you find it useful and can check it out if you have any questions, feel free to do so. to post it in the comments section below, so now let's go over division, let's say if you want to divide 56 by seven, what is the answer?

Now this can be written as 56 over 7 as a fraction, in both cases it represents division. Now the division is. the opposite of multiplication, so you need to ask yourself 7 times what number is equal to 56 again, you need to know the multiplication tables 7 times 8 is 56, therefore, 56 divided by 7 is 8. So let's try another example: What is 24 divided by 6? So, 6 times what number is equal to 24. I hope you have memorized your multiplication tables at this point, but take a minute to see if you can solve this without the use of a calculator. You can check your answer with the calculator although 24 divided by 6 is 4 because 6 times 4 is 24.

Okay, let's try one more example, so what is 42 divided by six or six times what number is forty-two? Alreadythat six times seven is forty-two, forty-two divided by six is ​​seven, so now it's your turn. feel free to try the following problems, so 20 divided by four 36 divided by six 72 divided by 8 and 144 divided by 12. So go ahead, take a minute and see if you can find the answers to those questions, then 20 divided by 4 is 5. because 4 times 5 is 20. since 6 times 6 is 36 36 divided by 6 is 6. now 8 times 9 is 72 so 72 divided by 8 is 9 and since 12 times 12 is 144 144 divided by 12 is 12 .try these 30 divided by five eighteen divided by two forty-eight divided by six and fifty-four divided by nine so 30 divided by 5 is 6. 18 divided by 2 is 9 since 9 times 2 is 18 and 48 divided by 6 is 8 and 9 times 6 is 54 so fifty-four divided by nine is six try this example four hundred divided by five now you might think this is out of your range but you can look at it this way 400 is 40 times 10 divided by 5. now What you could do is divide 10 by 5. 10 divided by 5 is 2 because 5 times 2 is 10 and we still have the 40.

So 40 times 2 is 80. Another way you could have looked at this is that you could focus on the 40. hence, 40 divided by 5. is 8 and then just add the zero and you can get 80. so try this 3500 divided by seven, so we divide 35 by seven, the first 35 divided by seven is five and then we add the two zeros, so thirty five hundred divided by seven is five 500. So what happens? this is 18,000 divided by 30 18 divided by 3 is six now we can cancel out a zero so we have two zeros left over let's move it so eighteen thousand divided by thirty is six hundred now how about 4,500 divided by 900 well we can cancel out the zeros , so this is basically 45 divided by f nine and since nine times five is forty-five, so forty-five divided by nine is five, so forty-five hundred divided by nine hundred, that's just five.

Now, how about six hundred thousand divided by twelve? one hundred, so let's cancel out the zeros, we can cancel out two zeros and if we divide sixty by twelve we get five, since five times twelve is sixty. Now there are two zeros left that we didn't take into account, so let's add those two zeros here. so therefore six hundred thousand divided by one thousand two hundred is five hundred now let's try this example sixty three thousand divided by seventy well we can cancel out zero 63 divided by seven is nine and we're going to add these two zeros therefore sixty and three thousand over seventy is nine hundred, so now let's say that if you have a number that doesn't fit into it, let's say like 39 over 6 6 and 39 that is not in the multiplication tables, then what can you do in a situation like This one, since 39 is not a multiple of 6, you can use long division to get the answer, so we're basically converting a fraction into a decimal.

The 39 will go inside the long division symbol. Now you must be wondering how many times 6 fits into 39. Well, if you write down all the multiples of 6 it's 6 12 18 24 30 36 42 is too much so let's get rid of that you need to add six six times to get to 36 since 6 times 6 is 36 and then you need to um, you need to subtract these numbers 39 minus 36 is 3. Now 6 doesn't go into 3, so we're going to add a 0. So we're going to add a decimal point and we're going to treat this as if it's 30. so 6 fits into 30 five times because we have to add six five times and jump to 30. so this shouldn't have been a zero here, it should have just put in a decimal point, but we're still going to bring down the zero, so 6 times 5 is 30 and we have a remainder of 0.

So the answer is 6.5, so that's an easy way to convert a fraction to a decimal, but let's try another example, let's try 42 divided by 8. How many times can 8 fit into 42? ? So let's write down the multiples of 8 16 24 32 40. 48 is too much, so if we add eight five times you get forty-eight times five is forty and we need to subtract forty-two less. Forty is two and we're going to add a decimal point to bring the zero down so how many times is eight to get to 20? eight goes into 20 at least twice three to be 24, so that's too many, so 8 times 2 is 16 and the difference of that will give us four and we need to add another zero so how many times is eight to forty?

As you can see, there are five, so we have to add eight five times to get to forty, so let's put in a five. here and eight times five is forty so the remainder is zero once you get a remainder of zero that's it you're done so the answer you're looking for is here so 42 divided by eight is therefore equal to 5.25, let's try another example, you can actually pause the video and try this one, so let's say if you want to know what 22 divided by 4 is, take a minute and try it yourself, how many times does 4 fit into 22?

So if we write the multiple of 4 is 4 8 12 16 20 24 is too much, then 4 goes into 22 at least 5 times, so 4 times 5 is 20 and the difference is 2. We're going to add a decimal point and then reduce a zero now. four fits into 20 five times, so we get another five and when we subtract these numbers the remainder is zero, so this is equal to 5.5, okay, so let's try, let's look at 28 divided by three, now three times six It's eighteen, three times nine is close. Twenty-seven three times ten is thirty, that's too much, so three goes into twenty-eight seven times, so now we have to subtract 28 minus the set 27 is one, let's add a decimal point and take down a zero, three goes into ten three . multiplied by three multiplied by three is nine and the difference is one, so you drop another zero and you get ten.

Notice that this process will repeat three times three is another nine, we will get one and therefore it is like nine point three three three three repeating so what you could write is just 9.3 with a line at the top that means 9.3 repeated. You can round it to 9.33 if you want, it's up to you. Now let's try dividing 47 by 5. So how many times does 5 go into 47? We know five. times nine is forty-five five times ten is too much, I'll be fifty-forty-seven divided by forty-five is two, so we need to add a decimal point since we don't have a remainder of zero and we need to add one here like Okay, now five goes into twenty-four times, so we get nine point four, and to practice, let's try one more example: 426 divided by 12.

So, how many times does 12 fit into 42 if we write the multiples of 12 is 12? 24 36 48 is too much so 12 fits in 42 at least three times 12 times 3 is 36 so 42 minus 36 is six lower the other six so how many times does 12 fit in 66? Well, let's continue adding multiples of 12. 48 plus 12 is 60 60 plus 12 is 72 that's too much, so we need 5 12 to get to 60. So 12 times 5 is 60. That gives us a remainder of six, so now we need add a decimal point. to go down a zero and we know that another five will give us sixty, twelve times five is sixty and this time the remainder is zero, therefore, um 426 divided by 12 is equal to this number which is 35.5, so now let's say If the numerator is smaller than the denominator, so let's say if you have a fraction like one over four, how do you convert that to a decimal so that the four is on the outside and the one is on the inside?

Well, four doesn't go into one, so let's add a decimal point and we'll add one here, so now let's treat the one as if it were ten, four divides into ten twice, so it's really a decimal here, but you can look at it like ten minus eight ten minus eight is two. we're going to add a zero, four goes in twenty-five times and the remainder zero, so one over four is equal to point two five. How about one out of three? This is one that's going to be repeated, so let's add a decimal point so three fits in. ten three times three times three is nine so ten minus nine is one add another zero three times ten three times so it's going to be nine and this will keep repeating so one over 3 is about 0.33 repeating now there are some common fractions that you just want to memorize, just If you want to know them, it can help you if you need to do a quick calculation, especially in your head, half is point five, two over two, as long as the numerator, which is the top of the fraction, and the denominator, which is the bottom of the fraction. fraction as long as they have the same value the value of the entire fraction is an integer is equal to one now here are some other numbers you want to know one over three is approximately point thirty-three two over three is like point six to six six repeating which you can actually round up to point sixty-seven and three over three as a whole, so it's equal to one a quarter is a quarter which is 0.25 which is the same as uh 25 2 4 is 0.5 which is approximately 50 3 4 is 0.75 as a percentage which is 75 percent and 4 over 4 which is an integer which is equal to 1 which is 100 percent so a fifth is point two and that's approximately twenty percent two over five is 0.4 just simply multiply 0.2 times 2 and you get 0.4 and that's like um set 40 3 over 5 that's point two times three which is point six and that's sixty percent and four over five which is equal to point eight which is eighty percent and you know. five over five is one now the other fractions you want to know are like one over eight one over eight is point one two five which is equal to twelve point five percent two over eight is point twenty five three over eight is point three seven five which is thirty and seven point five percent four eighths is point five or fifty percent and five over eight is uh 0.625 which is sixty two point five percent six over eight if you divide the six and the eight by two you get three quarters you can reduce the fraction which is equal to 0.75 or 75 percent and 7 8 is 0.875, which is 87.5 percent and then the last one you want to know is time, so one over ten is point one, which is ten percent. two out of ten, that's point two, which is twenty percent three out of ten, that's point three, which is thirty percent four out of ten point four, five out of ten point five, nine out of ten point nine, so you can see a pattern here and that's like ninety percent.

Now why is it useful? Well, sometimes you might not want to do long division. You can divide fractions in your head, like in that problem we had earlier. 39 out of 6. You can divide it into two smaller fractions. You know, 36 fits in six. like 36 over six now 39 minus 36 is three so 39 over six is ​​equal to 36 over 6 plus 3 over 6 because 36 plus 3 is 39 now by knowing the multiplication tables you know that 36 over 6 is equal to 6. now 3 over 6 you can reduce that if you divide both numbers by three at the top and bottom, everything you do at the top you have to do at the bottom of the fraction, so if we divide the top fraction by three, three divided by three is one, six divided by three is two. three over six is ​​equal to half and we know that half as a fraction is 0.5, so 6 plus 0.5 is 6.5 and that's what we got from long division when we divided 39 by 6.

The another example we had was 42 over 8. Now the highest multiple of 8 just below 42 is 40. So you want to separate this fraction, one of which will be a multiple of eight and the other is the remainder. 42 minus 40 is two, so two is the remainder. Now it's eight. in forty-five times or 40 divided by eight is five now two over eight we know that is the same as a quarter if you divide the top and the bottom by two you can reduce the fraction to a quarter and a quarter as a decimal we know that is 0.25, so we add 5 plus 0.25, which equals 5.25, so 42 over 8 is 5.25, so with this method go ahead and practice some problems, try nine over two and seven over three, convert it to a decimal and You can also convert it to a percentage.

Nine over two. We can divide it into eight over two plus one over two. Eight divided by two is four and one over two is point five, so this is equal to four point five. a percentage one is one hundred percent if you want to convert a decimal to a percentage multiply it by one hundred, so four point 4.5 is 450 percent. A Quaker method is to move the decimal point two units to the right to get 450. Now what? approximately seven over three, what is that as a decimal seven over three? We can divide it into six over three and one over three.

Now we know that six divided by three is two and a third is about point thirty-three, so we get two point thirty-three as a percentage which is 233 percent, so now let's try five over four and you can also try eight over five so pause the video and see if you can get the answer on paper so five over four we can rewrite it as four divided by four plus one over four now four divided by four that's just one and one over four is point two five so this is equal to one point two five or one hundred twenty-five percent eight over five um that's five over five plus three over five so five over five is one three over five is point six now, if you remember one over five, that's the point. two and then you multiply point two by three you get point six, so this is equal to one point six or 160, okay, let's not worry about the percentage anymore. convert the remainder to decimals, so try these two 15 over 2 and uh 19 over 3.

So we can do this fourteen over two plus one over two fourteen divided by two is seven, half is point five, so now it's equal at seven point five. three fits into nineteen six times three times six is ​​eighteenso we can write this as eighteen over three and one third eighteen divided by three is six one third is point thirty three so as a decimal this is six point thirty three so try these two 11 over 4 and 24 over 5. 11 over 4 is 8 over 4 and 11 minus 8 is 3, that's the remainder, so 8 over 4 is 2 3 4 is 0.75, therefore 11 divided by 4 is 2.75, so 24 over 5 is 20 over five plus four over five, so if you think about the multiples of five, that's five ten fifteen twenty-five is too much, it exceeds twenty-four, so we have to stop at twenty, that's why we choose this number and then to get this number, we simply subtract 24 minus 20. gives you the remainder four, so 20 divided by five is four and four over five is point eight, so 24 over 5 is 4.8 try this 23 over 8. so the multiples of 8 are 8 16 24 24 is too high, so we'll stop at 16. 23 minus 16 is 7.

So 8 16 divided by 8 is 2 and 7 8 is about a decimal 0.875, so this is 2.875, by the way, if you get 9 As a fraction, one over nine is approximately one point. one one one one repeating then two over nine is approximately point twenty-two repeating three over nine is point thirty-three repeating four over nine is point forty-four repeating five over nine point fifty-five repeating and so on so six over nine is point six six repeating eight over nine is like point eight eight repeated, so let's say if you have 15 over 99, that's going to be 0.15 repeated, so it's like .151515 and it goes on forever, so 27 over 99 It will be 0.272727 repeated, so you can write it. like just 0.27 so 46 over 99 and 73 over 99 this will be 0.46 repeating 0.73 repeating now let's say if you have like 246 over 999 this would be 0.246 repeating and if you have like 375 over 999 it's 0.375 repeating now some of these um you might be able to reduce this fraction, but if you want to quickly get the decimal value this is what it is just in case if it's based on nine now what about this?

What is 76 divided by one hundred? Now remember the last thing, actually before we do that, let's do this 76 divided by 10. Now when we said 5 over 10 we said it was 0.5 3 over 10 was 0.3 so what do you think 76 over 10 is equal to 76 over 10 is it equal to 7.6? What you have to do is move the decimal one unit to the left, so now it's right here you move it to the left and it becomes 7.6 so notice the pattern, so 76 over 10 is 7.6 76 over 100 you move the decimal 2 units to the left, that will be 0.76 76 over one thousand point zero seven six seventy-six over ten thousand is going to be .0076 so with that in mind divide these numbers by go ahead and simplify these fractions convert them to a decimal let's say yes you have 54 divided by 10 23 divided by 100 um 8 over 10 4.6 over 10 try that 54 divided by 10 is 5.4 23 divided by 100 is 0.23 so you move the decimal place two units to the left here just one unit eight divided by ten um that's point eight four point six divided by ten is point four six so try this point 43 divided by 10 7.1 divided by 10 84 divided by 100 and .25 divided by 100 so if you divide it by 10 move the point decimal one unit to the left so it's going to be .043 this is 0.071 actually that's too far that's 0.71 um this is going to be .84 and for this one I'm going to move it two units to the left so it's going to be .0025 so try with these 36 divided by one thousand four hundred seventy-five divided by one hundred three thousand eight hundred fifty. six divided by ten and uh 4.92 divided by a thousand so 36 divided by a thousand let's move the decimal point three units to the left one two three so it's point zero three six four hundred and seventy-five divided by a hundred move it two units to the left so this is four point seven five here this move one unit to the left so it's going to be 385.6 and for this one move it three units to the left one two three so we have to fit two zeros here the decimal point is now here so it's going to be point zero zero four nine two this is how you can divide numbers if it is ten hundred or thousand