In this video we're going to focus on just some basic topics in math. This is for those of you who really want to boost your math skills. So we're going to talk about how to add, subtract, especially when there's negative numbers.
How to multiply, do mental math in your head. We're going to go over the multiplication tables, the ones that you got to know. We're 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're going to talk about how to do percentages in your head, and how to simplify fractions mentally. We're also going to go over exponents, and even exponential fractions, order of operations. We're going to talk about square roots, how to simplify radicals, cube roots. We're going to go into scientific notation, how to convert it into 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 scientific notation number. Now we're also going to talk about how to solve equations, both linear equations, equations with decimals, fractions, um, equations involving radicals, cube roots, and...
also how to factor and use the quadratic equation and then after that we're going to talk about how to graph linear and quadratic equations and we'll go over some general parent functions and how to do some transformations so just some some of the common topics that you'll see in algebra but the beginning part of this video focus more mostly on arithmetic and then for those of you who are looking to do well in algebra the rest of the video might be of use to you so Let's begin. So let's start with some basic addition problems. If you want to add 5 plus 4, what is the answer?
Now for those of you who know, you know it's 9. But let's say... you don't know the answer to that problem what you could do is imagine a number line over here you have 0 on the left side negative 1 negative 2 negative 3 and so forth on the right you have 1 2 3 4 and 5 but now let's start from 5 let's say zeros over here and this is 5 Starting from 5 you want to add 4 if you wish to add you need to go to the right If you want to subtract you need to move to the left side So since you want to add 4 We're going to add we're going to go 4 units from the right so 1 2 3 4 and we're going to stop here So this is going to be 6 7 8 9 therefore 5 plus 4 is 9 let's try some other examples so what is 7 minus 3 7 minus 3 is 4 but let's prove it with the number line so let's say this is 0 and 7 is somewhere over here here if we start from seven and we wish 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 therefore seven minus three is four so what about this one 5 minus 8 what's the answer to that particular problem now 5 minus 8 is negative 3 so we're going to start at 5 And because we're subtracting, we're going to go 8 spaces to the left. So 1, 2, 3, 4. This would be 5, 6, 7, 8. So this is 4, 3, 2, 1, 0, negative 1, negative 2, negative 3. What's negative 4 plus 5? negative 4 plus 5 is positive 1 so if you start from negative 4 and since we're adding we're adding 5 to 4 we're going to go 5 units to the right so 1 2 3 4 5 negative 3 negative 2 negative 1 0 1 now you can also add it the other way to negative 4 plus 5 is the same as 5 minus 4 you can reverse the numbers this will also give you 1 so if you started at 5 and went for units to the left 1 2 3 4 you would end up at the same location which is 1 so try this one negative 8 plus 3 By the way, for these problems, feel free to pause the video, try it yourself, and see if you can get the answer. Negative 8 plus 3 is negative 5. So starting at negative 8, we're adding 3, so we're going to go 3 spaces to the right.
1, 2, 3. So negative 7, negative 6, negative 5. And there it is. now what about negative 9 minus 4 what's 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 to it, so we need to go 4 units to the left. So 1, 2, 3, 4. This is going to be negative 10, negative 11, negative 12, negative 13. Now what if there's like three negative signs, like negative 10 minus negative 4? Sometimes you might see this in parentheses, but it's the same as if it's written like this too. Now whenever you see two negative signs right next to each other with no number in between them, You can change that into a positive.
So this is the same as negative 10 plus 4. A negative times a negative is a positive. A negative times a positive is a negative. And a positive...
times a positive is just a positive number so what we have is negative 10 plus 4 so starting from negative 10 we're going to add 4 units or go 4 units to the right so 1 2 3 4 negative 9 negative 8 negative 7 negative 6 therefore negative 10 plus 4 is equal to negative 6 So what about 8 minus negative 3? How would you do that one? So we can change the two negative signs into a plus. So this is 8 plus 3, which we know is 11. If we start from 8 and go 3 units to the right, we would end at 11. So now let's take a quiz. Try these problems.
8 plus 7. 5 plus 9 6 plus 7 and 5 plus 12 So try these four problems first you can use the number line technique, and then I'm gonna pause the video Take a minute to do that And I'll just give you the answers so 8 plus 7 is 15 so if you go if you start from 8 and you go 7 units to the right you should end at 15 6 plus 7 is 13 5 plus 9 is 14 and 5 plus 12 is 17 try these let's say if you have nine minus four and 12 minus five and 14 minus six and one more that's similar to this type problem 22-13 so in these four problems notice that the positive number is larger than a negative number when that happens usually your result is going to be positive so not 9-4 is equal to positive 5. Using the number line, if you start at 9 and go 4 units to the left, since you're subtracting it by 4, this is going to be 8, 7, 6, 5. So 14-6, if you don't see that correctly, it looks like this. 14-6 is positive 8. And 12-5, that's positive 7. And 22-13 is positive 7. 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 math try these four problems 7 minus 9 4 minus 12 5 minus 16 and 8 minus 19 so notice that the negative number is larger this time so Therefore the result should be negative 7 minus 9 is negative 2 So if you start from 7, and if you travel 9 units to the left, this will be 6, 5, let's count it, 1, 2, 3, 4, 5, 6, 7, 8, 9. So this will be 6, 5, 4. 3 2 1 0 negative 1 negative 2 so we get that answer 5 minus negative 16 you should get negative 11 4 minus 12 is negative 8 and 8 minus 19 is Negative 11 as well, so let's use the number line for one more example Now let's use it for 4 minus 12 But counting 12 spaces backwards, that might seem like a long task. You could do it though, but we can also write it as negative 12 plus 4. That's the same as 4 minus 12. So, if we start at negative And if we go four units to the right, it's going to be 1, 2, 3, 4. So this is negative 11, negative 10, negative 9, negative 8. But if you want to do it the long way, you could start with 4 and go 12 spaces backwards.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. and as you can see you're going to reach negative 8 try these examples negative 6 plus 9 negative 5 plus 14 negative 8 plus 12 and negative 9 plus 17 so we have a positive and a negative number notice that the positive number is larger so when we add these two values we should get a positive value at the end so negative six plus nine is positive three using a number line if we start with negative six and if we go nine spaces to the right 1, 2, 3, 4, 5, 6, 7, 8, 9. This will be negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3. Negative 8 plus 12, that's going to equal positive 4. Negative 5 plus 14, that's 9. And negative 9 plus 17 will give you 8. so here's the next round of questions negative 5 plus 2 negative 12 plus 5 negative 16 plus 7 negative 14 minus 5 so try those so starting with negative 5 we're going to add two units so 1 2 we're going to go to units to the right and this will be negative 4 and negative 3 so negative 5 plus 2 is negative three so notice that the first number the negative one is larger so therefore the result will be negative negative 12 plus 5 is equal to negative 7 negative 16 plus 7 you should get negative 9 and negative 14 minus 5 is negative 19 try these what if so let's say if we have two negative signs negative 3 minus 5 what do you think the answer will be to that particular problem So, negative 3 minus 5 is negative 8. So, if we make the number line, starting at negative 3, we're going to subtract it by 5. So, we need to go 5 units to the left. 1. 2, 3, 4, 5. So this will be negative 4, negative 5, negative 6, negative 7, and negative 8. So when you have two negative numbers written in the way that we have it in this video, what you could do is just add 3 plus 5, which is 8, and then make a negative. So negative 8 minus 4 is the same as 8 plus 4 with a negative on the outside.
So what you could do is say 8 plus 4 is 12, and add the negative sign. To confirm it, we're going to start at negative 8, which is over here, and we're going to subtract it by 4. Or go 4 units to the left. 1, 2, 3, 4. So this is negative 9, negative 10, negative 11, negative 12. So negative 7 minus 6 is the same as 7 plus 6 with a negative on the outside.
7 plus 6 is 13, so this is negative 13. And this is going to be negative, and then 9 plus 8. So 9 plus 8 is 17, so this is going to be negative 17. try these negative 8 minus negative 3 negative 9 minus negative 15 negative 12 minus negative 4 and negative 14 minus negative 16. So whenever you see two negative signs like right next to each other you can make that into a positive number. So this is the same as negative 8 plus 3. So using the number line if we start at negative 8 we're gonna add three units to the right one two three so this is going to be negative seven negative six and negative five so negative nine minus negative 15 is the same as negative nine plus 15 and negative nine plus 15 is the same as 15 minus nine so you're gonna get positive six so you can reverse it if you want you So, negative 12 minus negative 4 is the same as plus 4. And negative 12 plus 4 is the same as 4 minus 12. And that should give you negative 8. Here we have negative 14 minus negative 16. So, that's negative 14 plus 16. And negative 14 plus 16 is the same as 4. 16 is the same as 16 minus 14 which equals 2 so keep that in mind you can always reverse the order if you have negative 3 plus 8 you can switch it the 8 is positive the 3 is negative so this is the same as positive 8 minus 3 which is just 8 minus 3 and that's equal to 5 so if you have like negative 10 plus 7 you can reverse and say you know what that's 7 minus 10 and the negative number is larger so when I subtract them I get 3 but since the sign of the larger one is negative this is going to be negative here the sign of the larger is positive so this is positive so that covers some basic addition but let's say if you want to add larger numbers let's say if you want to add a 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 the one we're going to put it in a next column and then we add 1 plus 2 plus 7 1 plus 2 is 3 3 plus 7 is 10 so 26 plus 74 is therefore 100 try this one add 35 and 62 so 35 plus 62 5 plus 2 is 7 3 plus 6 is 9 so this equals 9 997 Now what about 47 plus 65 so 47 plus 65 5 plus 7 is 12 you got to carry over the 1 and then 1 plus 4 is 5 5 plus 6 is 11 so this gives you 112 now what about subtraction so let's say if we wish to subtract 87 minus 23 so let's write it like this 87 minus 23 So, 7 minus 3 is 4, and then 8 minus 2 is 6, so this is equal to 64. Not bad, right? So you can see it here. 8 minus 2, 6, and then the 7 minus 3 is 4, so you get 64. what about this one 64 minus 39 so if we subtract 4 minus 9 we're gonna get a negative number so we don't want that actually let me put some space between these two numbers now what you could do is borrow a 1 from the 6 so the 6 turns into 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 that gives you 2 so therefore 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 take away or borrow a 1 from the 7. So that turns into a 6. So instead of having 6, we now have 16. So 16 minus 8 is 8. And 6 minus 4 is 2. So we get 28. now what about 125 minus 69 what is that equal to so let's borrow a 1 from 2 so now we have 15 15 minus nine is six and so this is not 11 and so now what we have here is 11 minus six is five so therefore 125 minus 69 is equal to 56 try this one 42 minus 68 notice that 68 is a bigger number than 42 so therefore the overall result is negative now you don't want to subtract it the way it's written what you could do is if you're subtracting by larger negative value reverse it 68 minus 42 so 8 minus 2 that's going to be 6 and 6 minus 4 is 2 since you reverse it add the negative sign so therefore 42 minus 68 is equal to negative 26 Let's try another example 25 minus 74 so we're subtracting 25 by a large and negative number so let's reverse it So 4 minus 5 we can't do that we need to borrow a 1 So the 7 will turn into a 6 and the 4 will become 14 so 14 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 go over multiplication. The first thing we're going to do is construct a simple multiplication table. So, let's begin.
Now, if you can construct the table yourself, it's going to help you to, like, know your multiplication numbers, which I would highly recommend you do so as well, because you'll see a pattern. So, for example, what's, like, what's 5 times 4? Now some of you may know the answer, but if you're not sure what that is, it might help for you to get a calculator or construct multiplication tables.
And you want to know your multiplication numbers up to 12. It's going to help you with a lot of arithmetic calculations that we're going to do from here on. So, don't skip this step. Now, I may not go up to 12 in this particular example, but I want to give you an idea of how to construct a table.
So, what we're going to do is put numbers in the first row. This is going to be 1, 2, 3, 4, 5, 6, 7, 8, 9. And here we're going to have 1, 2, 3, 4, 5, 6, 7. I guess we'll go up to 8 here. And maybe we can go up to 10. So 1 times 1 is 1. 1 times 2 is 2. And then these numbers will increase by 1. Now 2 times 1 is 2. 2 times 2 is 4. 2 times 3 is 6. And these numbers will continue. to increase by twos.
So notice the pattern. And so now for the threes. 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 we're just adding threes. Now 4 times 1 is 4, 4 times 2 is 8, 4 times 3 is 12, 4 times 4 is 16, 4 times 5 is 20, 4 times 6 is 24, 4 times 7 is 28, 4 times 8 is 32, 4 times 9 is 36, 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 5 times 5 is 25. 5 times 8 is 40 and 5 times 10 is 50 so these numbers will continue to add by 6 6 times 4 is 24 6 times 7 is 42 and so forth 7 times 1 is 7 7 times 3 is 21 7 times 6 is 42 7 times 8 56 and now for the 8 so this will keep increasing by 8 so let's say if you wish to multiply 6 times 8 so you look for you would go on the six row and stop once you reach the 8 column so 6 times 8 is 48 So now let's say if you want to multiply 7 times 9 so here's 7 here's 9 so from the seventh row go towards the ninth column and You get 63 so therefore 7 times 9 is 63 so let's say if we wish to multiply 4 times 6 so 4th row 6 column 4 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 arm yourself go up to 12 you want to know your multiplication numbers from 1 to 12 and then I'll quiz you on it. So let's say if you want to multiply 5 times 6. This can be written like this, or it can be written as 5 times 6. 5 times 6 is 30. Now, if you ever forget the table, what you could do is you can add 5 6 times.
Because that's what multiplication is. 5 times 6 means you're adding 5 6 times. And this will give you 30. So, for example, 4 times 3 is equal to 12. 4 times 3 means that you're adding 4 three times, and that's equal to 12. It can also mean that you're adding 3 four times. Which will also be equivalent to 12? so 5 times 3 According to the table is 15 But if you want to turn it into addition 5 times 3 is 5 plus 5 plus 5 3 times or It's adding 3 5 times and that gives you in both cases 15 So what's 6 times 4? 6 times 4 is 24. If you add 6 four times, you get 24 ok so at this point make sure you have the multiplication table memorize and then once you do try this quiz 8 times 7, just make sure you know it, is 56. 9 times 9 is 81. 7 times 6 is 42. 10 times 5 is 50. Okay, try these.
free to pause the video so 12 times 12 8 times 6 4 times 9 and 3 times 12 so 12 times 12 is 144 8 times 6 is 48 4 times 9 is 36 and 3 times 12 is also 36 So 12 times 5 that is equal to 60 7 times 9 is 63 8 times 12 is 96 and 11 times 11 is 121 Okay, let's try a few more problems, so what's 12 times 9? 5 times 8 5 times 11 7 times 12 12 times 11 and finally nine times eight so 12 times nine is 108 5 times 8 is 45 times 11 is 55 7 times 12 is 84, 12 times 11 is 132, 9 times 8 is 72. So make sure you're able to perform such multiplication. Now let's say if you have larger numbers.
Let's say if you wish to multiply 15 times 8. How would you do that? Well, you could do it the old-fashioned way, 15 times 8. 8 times 5, we know it's 40, so we're going to put the 0 and move the 4 to the top. And then you're going to multiply.
8 times 1 8 times 1 is 8 but we need to add the 4 so this is equivalent to 120 now if you have a calculator with you or you can go online and type in online calculating Google you can punch in this number in your calculator 15 times 8 is 120 now another way you can do this is you can break up the 15 into 10 plus 5 10 plus 5 is 15 and then multiply by 8 8 times 10 is 80 and 5 times 8 is 40 now 8 plus 4 is 12 if you add the 0 you get 120 so 80 plus 40 is 120 Let's try another problem. So what's 20 times 14? How would you multiply those two numbers? So 4 times 0 is 0. And then 4 times 2 is 8. Now we're going to add a 0. So 1 times 0 is 0. And 1 times 2 is 2. So if we add these...
numbers 0 plus 0 is 0 0 and 8 that's 8 and drop down the 2 we get 280 so another way to multiply 20 by 14 is picture in your mind if you have 14 $20 bills what's the value of 14 $20 bills you know 5 $20 bills is a hundred so another 5 of another 5 $20 bills is another hundred And then you have 4 leftover $20 bills. 4 20s is $80. So if you add this up, you have $280. And as you can see, you have 14 20s on this side.
5 plus 5 plus 4 is 14. When it comes to money, it's very easy to do math. Everyone understands it. Now another way you could have done this is you could separate the 14 into 10 plus 4. And 20 times is 200 if you have 1020 out bills as $200 and 20 times 4 well 2 times 4 is 8 so if you add the 0 you get 80 and then so this adds 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're gonna put the 5 here and add the two to the top five times two is 10 plus 2 that's 12 then we need to add a 0 5 times 1 is 5 and 5 times 2, I mean 1 times 2, that's 2. So if we add this, we get 5, 7, and 3. Now notice that we have two spaces after the decimal.
we need two spaces here after decimal so this is 3.75 so that's how you can multiply a number in the decimal another way to multiply 15 by 25 is we know point 25 is 25 cents imagine if you have quarters 15 quarters has a value of 375 for every four quarters you have as a dollar so 4 times 25 cents that's one dollar another four quarters is a dollar Another set of four quarters is dollar so that's 12 quarters that we have so far and Then 15 quarters we need three more so the remaining three quarters is 25 cents I mean 75 cents So you have three dollars and 75 cents yeah if you add these numbers if you add these you have a total of 15 quarters 4 plus 4 plus 4 plus 3 is 15 so let's say if you want to multiply 8 times 17. So try this problem, but using both techniques. So let's do it this way, 17 times 8. So 8 times 7, that's 56. We're going to 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 8 times 10 is 8. 80 and 8 times 7 is 56. If you add these two numbers, 80 and 56, 6 plus 0 is 6, 8 plus 5 is 13, you get the same answer 136. So there's many techniques that you can use to do mental math or even just math on paper without the use of a calculator. But now let's go over some other concepts. Let's see if you want to multiply 10 times 10. Now, by instinct, you probably know that this is 100. But the way you should do this is, in your mind, you should multiply 1 times 1, which gives you 1, and then add the two zeros.
So, for an example, 10 times 100. Well, if we multiply 1 and 1, we get 1. And then add the three zeros that we see. We have 1, 2, 3 zeros, so 1 means 0, 0, 0. So that's 1,000. So, 100 times 100. So, 1 times 1 is 1. And then add the four zeros. so we get 10,000 so what do you think a hundred times ten thousand is well here we have a total of six zeros so this is 1 million Okay, so now let's try this principle to other harder problems. Let's say if you want to multiply 50 times 100. So basically, if you have 50 $100 bills, how much money do you have?
So, if we multiply the numbers on the outside, 5 and... one five times one is five and then add the three zeros this is five thousand if you want to multiply 40 by 200 what you do first is multiply four times two and that's going to give you eight and then add the three zeros so therefore 40 times 200 is 8,000 so what's 30 times 600 well 3 times 6 is 18 and if we add the three zeros that's 18,000 so what about 70 times 800 7 times 8 is 56 add the three zeros That's 56,000. Okay, so let's try a quiz. So try these problems.
So, these large calculations, you can do without the use of a calculator. So, 40 times 900 seems like you're multiplying very, very huge numbers. But remember, all you need to do is multiply the numbers on the outside. 4 times 9 is...
36 and then add the three zeros so therefore 40 times 900 is 36,000 so what's 500 times 700 so 5 times 7 is 35 and then we have four zeros to add. So this is going to be 350,000. 60 times 40. So 6 times 4 is 24. Add the zeros.
This is 2,400. What's 8 times 5? 8 times 5 is 40. Then add the 6 remaining zeros.
So this is equal to 40 million. 12,000 times 70,000. Now this is why you want to know your multiplication tables up to 12. 12 times 7 is 84. And we have 3 zeros on this side.
And 4 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 12,000 times 70,000 is 840 million. So regardless of how big these numbers get, as long as you follow the basic principles, you can pretty much do math up to any limit. By the way, the video that you're currently watching is a one hour trailer version of a longer four hour paid video.
So I'm going to post a link here in case if you want to watch the remaining three hours of this video. find it useful and you can check that out if you have any questions feel free to post it in the comment section below so now let's go over division let's say if you wanted 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 division is the reverse of multiplication so you need to ask yourself 7 times what number is equal to 56? Again, you need to know your 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? So hopefully you have your multiplication tables memorized at this point.
But take a minute and see if you can figure this out without the use of a calculator. You can check your answer with the calculator though. 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 6 or 6 times what number is 42 since 6 times 7 is 42 42 divided by 6 is 7 so now it's your turn feel free to try the following problems so 20 divided by 436 divided by 672 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 so 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 5, 18 divided by 2. 48 divided by 6 and 54 divided by 9 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 54 divided by 9 is 6 Try this example.
400 divided by 5. Now you might think this is outside of your range, but you can view 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 seen this is you could focus on the 40 right here 40 divided by 5 is 8 and then simply add the 0 you can get 80 so try this one 3500 divided by 7 so let's divide 35 by 7 first 35 divided by 7 is 5 and then add the two zeros so 3500 divided by 7 is 500 so what about this one what's 18,000 divided by 30 18 divided by 3 is 6 now we can cancel a 0 so we have two zeros left over we're going to carry it over so 18,000 divided by 30 is 600 now what about 4,500 divided by 900. Well, we can cancel the zeros. So this is basically 45 divided by 9, and since 9 times 5 is 45, then 45 over 9 is 5. So 4500 over 900, that's just 5. Now what about 600,000? divided by 1,200. So let's cancel the zeros.
We can cancel two zeros. And if we divide 60 by 12, we get 5, since 5 times 12 is 60. Now there's two zeros remaining that we didn't account for, so we're going to add those two zeros here. So therefore, 600,000 divided by 1,200 is 500. Now let's try this example 63,000 divided by 70. Well we can cancel 0. 63 divided by 7 is 9 and we're going to add these two zeros.
So therefore 63,000 over 70 is 900. So now let's say if you have a number that doesn't go into it. Let's say like 39 over 6. 6 and 39 that's not in the multiplication tables. So what can you do in a situation like this?
Since 39 is not a multiple of 6, you can use long division to get the answer. So basically we're converting a fraction into a decimal. The 39 is going to go inside the long division symbol. Now you have to ask yourself, how many times does 6 go into 39?
Well, if you write out all the multiples of 6, it's 6, 12, 18, 24, 30, 36. 42 is too much, so we're going to get rid of that. You need to add 6 six times to get to 36, since 6 times 6 is 36. and then you said they 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 goes into 30 5 times, because we had to add 6 5 times to get to 30. So this shouldn't have been a 0 here. I should have just put just a decimal point.
But we're still going to bring down the 0. 6 times 5 is 30, and we have a remainder of 0. So the answer, therefore, is 6.5. So that's a simple way in which you can convert a fraction into a decimal. But let's try another example.
Let's try 42 divided by 8. So, how many times does 8 go into 42? So, let's write out the multiples of 8. 8, 16, 24, 32, 40. 48 is too much. So, if we add 8 five times, you get to 40. 8 times 5 is 40. And we need to subtract.
So 42 minus 40 is 2. And we're going to add a decimal point. Bring down the 0. So how many times does 8 go into 20? 8 goes into 20 at least 2 times.
3 times would be 24, so that's too much. So 8 times 2 is 16. And the difference of that will give us 4. And we need to add another 0. So how many times is 8 going to 40 as you can see it's 5 times We got to add 8 5 times to get to 40 So we're gonna put a 5 here and 8 times 5 is 40 so the remainder is 0 once you get a remainder of 0 That's it. You're done. So the answer that you're looking for is right here So 42 divided by 8 is therefore equal to 5.25 let's try another example actually you can pause the video and try this one so let's say if you want to find out what 22 divided by 4 is so take a minute and try it yourself So how many times does 4 go into 22?
So if you write out the multiples of 4, it's 4, 8, 12, 16, 20, 24 is too much. So 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 bring down to 0 now 4 goes into 25 times so we get another 5 and when we subtract these numbers the remainder is 0 so this is equal to 5.5 alright so let's try let's see 28 divided by 3. Now, 3 times 6 is 18. 3 times 9 is close, is 27. 3 times 10 is 30. That's too much.
So, 3 goes into 28 7 times. So now we have subtract. 28 minus 27 is 1. We're going to add a decimal point and bring down a 0. 3 goes into 10 three times.
3 times 3 is 9. And the difference is 1. So you bring down another 0, you get 10. Notice that this process will repeat. 3 times 3 is another 9, we're going to get 1, and therefore it's like 9.33333 repeating. So what you could write is just 9.3 with a line on top, which means 9.3 repeating. You can round it to 9.33 if you want, it's up to you.
So now let's try... 47 divided by 5 So how many times is 5 going to 47? We know 5 times 9 is 45. 5 times 10 is too much, that would be 50. And 47 divided by 45 is 2. So we need to add a decimal point since we don't have a remainder of 0. And we got to add one here as well.
Now 5 goes into 20 4 times. So we therefore get 9.4. And for the sake of practice, let's try one more example.
426 divided by 12. So how many times does 12 go into 42? If we write out the multiples of 12, it's 12, 24, 36. 48 is too much, so 12 goes into 42 at least 3 times. 12 times 3 is 36. So 42 minus 36 is 6. Bring down the other 6. So how many times does 12 go into 66?
Well, let's keep 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 up to 60 so 12 times 5 is 60 so that gives us a remainder of 6 so now we need to add a decimal point we're going to bring down a 0 and we know another 5 will give us 60 12 times 5 is 60 and this time the remainder is 0 so therefore 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 1 over 4. How do you convert that into a decimal?
So the 4 is on the outside and the 1 is on the inside. Well, 4 doesn't go into 1, so let's add a decimal point. And we're going to add 1 here.
So now let's treat the 1 as if it's a 10. 4 goes into 10 two times. So there's really a decimal here, but you can view it as 10 minus 8. 10 minus 8 is 2. We're going to add a 0. 4 goes into 20 five times, and the remainder is 0. So 1 over 4 is equal to 0.25. What about 1 over 3? This is one that's going to repeat.
So let's add a decimal point. So 3 goes into 10 three times. 3 times 3 is 9. So 10 minus 9 is 1. Add another 0. 3 goes into 10 three times. So that's going to be 9, and this is just going to keep repeating.
So 1 over 3 is about.33, repeating. Now there are some common fractions that you simply want to commit to memory. You just want to know them. It can help you if you need to do a quick calculation, especially in your head.
1 half is 0.5. 2 over 2. Whenever the numerator, which is the top part of the fraction, and the denominator, which is the bottom part of the fraction, whenever they have the same value, the value of the entire fraction as a whole is equal to 1. Now here's some other numbers you want to know. 1 over 3 is about 0.33. 2 over 3 is like 0.666 repeating, which is really, you can round it to 0.67. And 3 over 3 is a whole, so that's equal to 1. 1 fourth is a quarter, that's 0.25, which is the same as 25%.
2 fourths is 0.5, which is about 50%. three fourths is 0.75 as a percent that's 75% and 4 over 4 that's a whole that's equal to 1 which is a hundred percent so 1 fifth that's.2 and that's about 20% 2 over 5 is.4 you simply just multiply.2 times 2 and you get.4 and so that's like um sets 40% 3 over 5 that's 0.2 times 3 which is 0.6 and so that's 60% and 4 over 5 That is equal to 0.8 which is 80% and you know 5 over 5 is 1 now the other fractions that you want to know is like 1 over 8 1 over 8 is point 1 2 5 which is equivalent to 12.5 percent 2 over 8 is point 25 3 over 8 is 0.375, which is 37.5%. 4 eighths is 0.5, or 50%, and 5 over 8 is 0.625, which is 62.5%.
6 over 8. If you divide the 6 and the 8 by 2, you get 3 fourths. You can reduce the fraction, which is equal to 0.75, or 75%. And 7 eighths is 0.875, which is 87.5%. And then the last one you want to know is the tens.
So like 1 over 10 is 0.1, which is 10%. 2 over 10, that's 0.2, which is 20%. 3 over 10 is 0.3, which is 30%.
4 over 10, 0.4. 5 over 10, 0.5. 9 over 10, 0.9. So you can see a pattern here, and that's like 90%.
So now, why is this useful? Well sometimes you may not want to do long division, you can divide fractions in your head. So like, for example, that problem that we had before, 39 over 6, you can break that down into two smaller fractions. You know 36 goes into 6, so you can write it as 36 over 6. Now, 39 minus 36 is 3. So, 39 over 6 is equal to 36 over 6 plus 3 over 6, because 36 plus 3 is 39. Now, by knowing your multiplication tables, you know 36 over 6 is equal to 6. Now, 3 over 6, you can reduce that.
If you divide both numbers by 3, top and bottom, whatever you do to the top, you must... due to the bottom of the fraction. So if we divide the top fraction by 3, 3 divided by 3 is 1, 6 divided by 3 is 2, 3 over 6 is equivalent to 1 half and we know 1 half as a fraction is 0.5. So 6 plus 0.5 is therefore 6.5 and that's what we got for long division when we divided 39 by 6. The other example that we had was 42 over 8. Now the highest multiple of 8 just under 42 is 40. So you want to separate this fraction, one of which will be a multiple of 8. and the other is the remainder 42 minus 40 is 2 so 2 is the remainder now 8 goes into 45 times or 40 divided by 8 is 5 now 2 over 8 we know that to be the same as 1 fourth if you divide the top and the bottom by two you can reduce the fraction to 1 4th and 1 4th as a decimal we know it's 0.25 so therefore we add 5 plus 0.25 which is equivalent to 5.25 and so 42 over 8 is 5.25 so with this method go ahead and practice a few problems try 9 over 2 and 7 over 3 converted into a decimal and you can also convert it to a percentage as well 9 over 2, we can break it into 8 over 2 plus 1 over 2. 8 divided by 2 is 4, and 1 over 2 is 0.5, so this is equal to 4.5.
By the way, as a percentage, 1 is 100%. if you want to convert a decimal into a percentage and multiply by 100 so 4.5 is 450 percent a quick method is you can move the decimal point two units to the right so you get 450 Now what about 7 over 3? What is that as a decimal?
7 over 3, we can break that into 6 over 3 and 1 over 3. Now we know 6 divided by 3 is 2, and 1 third is about.33, so we get 2.33. As a percentage, that's 233%. So now let's try 5 over 4 and you can also try 8 over 5 so pause the video and see if you can get the answer on paper.
So 5 over 4 we can rewrite that as 4. 4 divided by 4 plus 1 over 4. Now, 4 divided by 4, that's just 1, and 1 over 4 is 0.25, so this is equal to 1.25, or 125%. 8 over 5 that's 5 over 5 plus 3 over 5 so 5 over 5 is 1 3 over 5 is 0.6 now if you remember 1 over 5 that's point 2 and then you multiply points 2 by 3 you get 0.6 so this is equal to 1.6 or 160 percent okay let's not worry about the percentage anymore let's just convert the rest into decimals so try these two 15 over 2 and 19 over 3 so we can make this 14 over plus 1 over 2 14 divided by 2 is 7 1 half is 0.5 so this is equal to 7.5 now 3 goes into 19 6 times 3 times 6 is 18 so we can write this as 18 over 3 and 1 third 18 divided by 3 is 6 1 third is 0.33 so as a decimal this is 6.33 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 2 is 0.75 five so therefore 11 divided by 4 is 2.75 so 24 over 5 that's 20 over 5 plus 4 over 5 so if you think of the multiples of of 5 that's 5 10 15 20 25 is too much it exceeds 24 so we need to stop at 20 that's why we choose this number and then to get this number simply subtract 24 minus 20 it gives you the remainder 4 so 20 divided by 5 is 4 and 4 over 5 is 0.8 so that therefore 24 over 5 is 4.8 try this one 23 over 8 so multiples of 8 are 8 16 24 24 is too high so we'll stop at 16 23 minus 16 7 so 8 16 divided by 8 is 2 and 7 8 it's about as a decimal point 8 7 5 so this is 2.8 7 5 By the way, if you get like 9 as a fraction, 1 over 9 is about 0.1111 repeating. So 2 over 9 is about 0.22 repeating. 3 over 9 is 0.33 repeating. 4 over 9 is about 0.133 repeating.
is.44 repeating 5 over 9.55 repeating and so forth so 6 over 9 is.66 repeating 8 over 9 is like.88 repeating so let's say if you have 15 over 99 that's going to be 0.15 repeating so it's like 0.15 1515 it keeps on going forever so 27 over 99 it's going to be 0.27 2727 repeating so you can write it as just 0.27 So, 46 over 99, and 73 over 99. This will be.46 repeating,.73 repeating. Now, let's say if you have like 246. Over nine nine nine this would be point two four six repeated and if you have like 375 over nine nine nine It's point three seven five repeating Now some of these may be able to reduce this fraction but if you quickly want to get the decimal value this is what it is so just in case if it's based on 9 now what about this one what's 76 divided by 100 Now, remember the last... Actually, before we do that, let's do this one. 76 divided by 10. Now, when we said 5 over 10, we said that was 0.5. 3 over 10 was 0.3.
So what do you think 76 over 10 is equal to? 76 over 10 is equal to 7.6. You see, what you need to do is move the decimal one unit to the left.
So it's right now, it's right here. You move it to the left, it becomes 7.6. So notice the pattern. You see, it's right here. So, 76 over 10 is 7.6.
76 over 100, you move the decimal two units to the left, that's going to be.76. 76 over 1,000,.076. 76 over 10,000, it's going to be.0076.
So, with that in mind, divide these numbers by... Go ahead and simplify these fractions, convert them into a decimal. Let's see if... if you have 54 divided by 10 23 divided by 100 8 over 10 4.6 over 10 try those So 54 divided by 10, that's 5.4. 23 divided by 100 is 0.23.
So you move the decimal place two units to the left. Here it's just one unit. 8 divided by 10, that's 0.8. 4.6 divided by 10 is 0.46.
so try this point 43 divided by 10 7.1 divided by 10 84 divided by 100 and point 25 divided by 100 so if you divided by 10 move the decimal point one unit to the left so this is going to be point zero four three this is point zero seven one actually not too far that's point seven one this is going to be point eight four and for this one I can move it two units to the left so it's going to be point zero zero two five So try these 36 divided by a thousand 475 divided by 100 3856 divided by 10 and 4.92 divided by a thousand so 36 divided by a thousand let's move the decimal point three units are left one two three so it's point zero three six four hundred seventy five divided by a hundred move it to units to left so this is four point seven five here this move it one unit to left so it's going to be three hundred eighty five point six now for this one move it three units to left one two three so we got to fit in two zeros here the decimal points now here so it's going to be point zero zero four nine two so that's how you can divide numbers if it's ten a hundred or a thousand