[Music] [Music] hi welcome to mega math I'm Scott Branzburg also known as the human calculator and I'd like to welcome you to a whole new type of program that really makes math fun all I'm going to do today is show you different ways to look at numbers hopefully to make math easier for you so you can use numbers in everyday life a little bit more and a little bit better now before we get started I'd like to explain to you how to use the program you're going to receive in your program of mega math a video for audio cassettes along with a workbook what I'd like you to do now is take out your workbook and open it up to the Edition section of the workbook now we're going to go through in this video addition subtraction and multiplication all kinds of different ways to make numbers easier and I'll show you some neat shortcuts and tricks so you can actually do some of the stuff in your head or if you have to do it on paper you'll be able to do it without actually writing everything down and carry everything it'll be a lot easier for you the rest of the program will include fractions and decimals percentages 92 steps to algebra a little bit of taxes and tipping and how to make change and perpetual calendars all kinds of things that you'll be able to use in everyday life but the first thing I want you to do is really take the time to practice your addition subtraction and multiplication because this is the basis or foundation that you'll use to get through the rest of the program and make it much easier for you let's start off with addition addition is used in everyday life all the time and I think it's the most simplest thing to learn so let's take the time now to teach you how to add from left to right it's actually opposite of the way you were taught in school all right I'm gonna give you a couple of examples let's start out with 14 plus 15 now the basic way that you learn how to add you always start on the right and you add them up and then you go over here and you add them up and you're surprised you get an answer I'm going to show you how to go left to right backwards and it eliminate the carrying and you'll see how that works in a minute but first off let's start right here this one right there is in the tens column so I stands for ten and this is also in the tenth column so that stands for ten so what I do is I start adding left to right going down the Combes this way so what's ten plus ten the answer is 20 and then you just go up here to the first number in the next column so 20 plus 4 would give you 24 plus 5 would give you an answer of 29 and simply enough that's the answer 29 all you have to do is read it left to right and keep a running total it's called a base number let's try another one how about 23 plus 13 now the first thing we do is we start on the left now this is an attempt column this 2 so that means 2 tens or 20 and then down here this one stands for 10 so what's 20 plus 10 20 plus 10 is 30 and then you go to the next column 30 plus 3 would give you 33 plus 3 more would give you 36 and that's the answer let's try one more how about 32 plus 25 now a little bit bigger first thing we do is we come up here to the top left corner there's a floor there stands for four tens or forty this tomb stands for two ten or twenty so let's add those together first what's 40 plus 20 the answer is 60 and now we just go to the next column 60 plus 2 is 60 2 plus 5 is 67 and that's the answer so you can see how it works all you do is you start on the left going to the right keeping a running total out loud sort of in your head all right so let's try some more numbers but this time I'm going to show you how to carry when you carry numbers it really doesn't matter how you do it because there's no such thing as carrying when you go left to right let me give you an example 24 + 17 now we start on the left again let's go here this 2 stands for 20 this is 10 so what's 20 + 10 30 and then we come up here to this column what's 30 + 4 34 + 7 so now someone use your failures some of you might break it down to 6 & 1 but 34 plus 7 equals 41 so the answer is 41 no carrying you just go from the 30s to the 40s just by adding to your base number let's try another one how about 28 plus 14 starting on the left this is 20 this is 10 what's 20 plus 10 the answer is 30 and then we go to the next cone what's 30 plus 8 the answer is 38 plus 4 more 38 plus 4 what's that you should get 42 so the answer is 42 as you can see you don't carry you just keep adding to that base number it just takes a little bit of practice so I want to give you one more example before we get into even bigger numbers how about 39 plus 13 starting on the left 30 plus 10 would give you 40 and then up to the next column what's 40 plus 9 49 and then we add the three what's 49 plus 3 you should get 52 so as you can see you never carry you always know what the answer is going to be about right away because you're working with the most significant numbers first the tens instead of the ones and what really is the biggest advantage to learning how to add left to right is the fact that you're understanding how tens and ones work together and how they add together without carrying so I'd like to give you one more example but this time let's try a bunch of through two-digit numbers and addemup and a column like form for example 24 15 31 and 17 a lot of numbers we're going to go left to right down the columns okay so this 2 right here stands for what that stands for 20 this one stands for 10 so what's 20 plus 10 you should get 30 and then we add the next number which is 3 or 30 more what's 30 plus 30 you should get 60 and then the next number is a pen so what's 60 plus 10 you should get 70 and now we come up to the next column what's 70 plus 474 add 5 more what do you get 79 add one more 79 plus 1 which give you 80 and then 7 more is 87 so the answer to 24 plus 15 plus 31 plus 17 is 87 and all you did was keep a running total in your head left to right and you never have to carry it totally eliminates carrying so what I want you to do now is go to your workbook and you'll see a whole list of example that I want you to practice this technique this left-to-right edition with two-digit numbers make sure that you understand how to go down two columns left to right and you understand that there's no carrying and work on practicing keeping your base number and continually adding to that to get to the answer good luck [Music] all right you just finished two digits addition in the workbook and hopefully understood it very well and you can just fly through those now if you're still having a little bit of trouble with it or it's just not making sense to you practice a little bit more go back into the workbook read through it again and try the exercises one more time just to make sure you're really sure that you understand it but if you already have done that and you really feel confident let's move on a three-digit addition a little bit tougher but it's not really once you get into it I'm going to show you some shortcuts how to group a little bit make it a lot easier so let's start out with an easy example how about 243 plus 125 now same concept we're going to go left to right except this time instead of starting at the tens column there's another column out here that's called the hundreds column when there's three digits you have the hundreds tens ones so we're going all the way out to the left this is the hundreds that two right there just stands for two hundred and underneath it is a one which stands for one hundred so now add those up what's 200 plus 100 you should get 300 and then we go up to the next column this is the tenth cone so if for just means 40 so what's 300 plus 40 the answer is 340 and then we add 20 more and you should get 340 plus 20 is 360 and then we just go to the next column what's 360 plus 3 the answer is 360 3 and then 5 more because these little ones column so what's 363 plus 5 you should get 368 and that's the right answer so you see how easy it is it's the same concept as two-digit addition just remember when there's three digits you're working with the hundreds first then the tens and then the woods let's get let's give it another shot I'm going to give you a little bit harder let's do a 256 plus 213 now same idea left to right but you're starting with the hundreds remember so what's 200 plus 200 that should be 400 and now you move up to the next column what's 400 plus 50 450 and then add 10 more you'll get 460 and then you just go to the next column what's 460 plus 6 466 and then add three more 469 is the correct answer that's what you should get now you might be noticing now that it's hard for you to remember the base number as you're going through the examples here's what you do you're already saying it to yourself to keep remembering it that's all I do is I'm going to hundred 400 450 460 466 469 I already say the whole number every time just don't go 400 okay that's 50 60 60 that's going to mess you up and you're going to forget what you had over here all right so let's try another one how about 352 plus 145 left to right starting with the hundreds 300 plus 100 gives you four hundred plus 50 400 plus 50 should give you 450 add 40 more what's 450 plus 40 490 and then just go to the ones column what's 490 plus two 492 plus five should give you 497 it's that simple and if you continue to practice left to right adding to that base number it'll start to make sense to your brain and it will be easier to remember the numbers as you're going through it just by repeating it over and over again as you add to that base number now what happens if you have to carry let's try three to do numbers with a little bit of a carry just to see how you do and remember you don't really care you just keep adding to that base so let's try 147 plus 124 starting from the left obviously this is 100 this is 100 what's 100 plus 100 you'll get 200 then you go to the tens this for right here stands for 40 so it's 200 plus 40 240 add 20 more you'll get to 60 then we go to the one what's 260 plus 7 you'll get 267 and then we're going to add four more what's 267 plus 4 the answer is 271 see again how you don't even carry you just keep adding to that base number and I have to keep reminding you always say the whole base number don't just say the tens or the hundreds alone say the whole thing every time let's try another one what's 256 plus 125 starting on the Left 200 plus 100 how much is that 300 up to the 50 what's 300 plus 50 350 add 20 more 370 and then we go to the one what's 370 plus 6 376 and now we add five more what's 376 plus five you should get 381 all right and now I want to try one more example a little bit harder 249 plus a hundred and thirty-two left to right starting with the hundreds keeping a running total saying the whole number every time two hundred plus 100 will give you three hundred and then we go to the tens that's a 40 right so what's three hundred plus forty three forty add 30 more what do you get three 40 plus 30 you should get 370 and then we go to the next column what's 370 plus 9 379 and then add two more what's 379 plus two the answer is 381 hopefully by now you're starting to see how it works where you just keep that running total keep that base number and just keep adding to it and as we get into bigger numbers you'll see how much more effective this is because you don't care no matter how large numbers get so what I want to do now before you go into a workbook to complete this part of the program I want to give you one more example with a column of three-digit numbers I just want you to give it a try and you'll still see there's no carrying it all just has to do with keeping that base number going let's try a my favorite example 123 216 121 and 214 I always use this example because it's easy to learn how to carry with a column of numbers instead of starting over here now because I want you to realize something too if you start over here now as you've been doing it left to right watch what happens when you go right to left 3 + 6 is 9 10 14 write down a 4 carry a 1 and then you add up 3 4 6 7 and then you add up 1 3 4 you have no idea what the answer is going to be until the very end notice how easy it is when you're left to right Uman right away this is 600 600 something it's going to be maybe 6 or 700 but right away you had a good estimation of the answer that's one of the keys of adding left to right so let's try this this is one hundreds column that's a 100 this is a 200 get your running total base number going once 100 200 300 add another 100 and you'll get 400 200 more will give you 600 now we go to the tens column that's a 20 right there that's a 10 that's the 20 that to 10 right so what's 600 plus 20 620 add 10 more you should get 630 how about 20 more you should have 650 and then 10 more will give you a total of 660 so far now you've got 660 and you go to the ones now go small through this 660 plus 3 is how much 663 add six more you should get 669 all right and now we're going to add one more what's 669 plus one 670 and then four more 670 plus 4 will give you 674 that's the answer to 123 plus 216 plus 121 plus 214 and remember you never carried just give this a little bit of practice go back into your workbook go through all the examples make sure you get them all right and make sure you understand how you're carrying the numbers without carrying you're just adding to that base number and practice remembering that base number that's the hardest part but it's really easy once you get into it [Music] subtraction does not exist I'm trying to teach you how to do shortcut math and the first thing I want you to realize is that subtraction is really difficult to learn it doesn't make sense to our brain so what I introduce to people when I teach them how to do subtraction is I teach them reverse addition let me give you an example if I said to you 15 minus 6 instead of looking at that as a subtraction problem I always look at it backwards upside down what Plus this will give me this because in all subtraction problems this number Plus this number always that up to the top number so I always look at it backwards so instead of borrowing from the 1 or anything like that I just say ok 15 minus 6 well they're saying to me 6 plus what equals 15 and then I know 6 plus 9 is 15 same thing if I said 24 minus 19 now you could do it and look at it this way the regular subtraction way and say well 20 minus 10 is 10 and it oops I got to borrow so before you get into that just read the problem and turn it around so instead of saying 24 minus 19 why not say 19 plus what equals 24 and then you know right away just five more so the answer is five it's better borrowing and all that stuff if the numbers aren't that big try to reverse the problem and do it upside down let me give you one more example how about 32 minus 18 now a little bit farther apart and the number here is still bigger than this number all right so before you get into going 32 borrow because because this 2 is too small for this look at it this way 18 plus what equals 32 18 plus 1 equals 32 if you're pretty good numbers or if you're good at adding because we just did a whole chapter on addition you should get the answer of 14 what I'm going to show you in subtraction though is how to actually go left to right doing subtraction so open up your workbooks to the subtraction section and let's go through that together let's get into left-to-right subtraction now it's the same concept as left-to-right addition except it gets a little tricky when you've got to sort of get into a borrow situation so we'll go through it real slow and make sure you understand each step along the way let me give you some examples the first thing I'm going to do is some basic subtraction left to right without any borrowing let's try on 26 minus 14 this is a whole different way of looking at subtraction because you're using the whole number instead of just learning how to subtract digits and borrow this will teach you how to look at the whole problem 26 minus 14 let's start over here then obviously is 20 and this is 10 so what's 20 minus 10 10 and then you go to the right column what's 6 minus 4 2 so the answer is 12 10 into is 12 let's try another one 38 minus 27 starting on the left what's 30 minus 20 10 and then once 8 minus 7 one so we have 10 + 1 or 11 you always keep a running total in your head again but you just do a one step at a time and make sure you understand the whole problem don't try to just read it one line at a time understand you're doing the whole problem at the same time in your head let's try one more what's 45 minus 33 now sorry on the left what's 40 minus 30 once again we get 10 and then 5 minus 3 is 2 to give us an answer of 12 pretty simple the best thing about going left to right though and subtraction is that right away you knew the answer is going to be about 10 or 15 maybe but you knew right away what it was about to be doing it the other way just know that it ends in a 2 which you have no idea what's over here so once again estimation skills will increase using this technique now let's try some with a little bit of a borrowing situation in this case let's do on 26 minus 17 pretty big problem 26 minus 17 to start you're go left to right what's 20 minus 10 you've got 10 right now here's where it gets tricky as soon as you see that this number is bigger or smaller than this number all right this is smaller than this number whenever the smaller numbers on top that means you have to borrow normally but what you're going to do is just say okay well I've got 210 from here right so add it to this instead of having at 6 you've got 16 minus 7 what's 16 minus 7 you should get 9 and that's the answer let me go through another one and try it again how about 34 - I'm going to make it tough 19 okay just to show you how this works 30 minus 10 is how much you should get 20 now so we've got a 20 you've got to keep that in our head the running total base number you've got 20 now come up here you see that this number is smaller than this number so there's a borrowing situation normally so we've got 20 over here right just add it to the top number what's 20 plus 4 you should get 24 and now we just - this 9 so what's 24 minus 9 the answer is 15 now if you have problems subtracting 24 minus 9 there's an easier way to do it I'm going to just do a little note up here 24 minus 9 if you get to that situation if you have 12 or that make this 9 a 10 it's much easier to subtract and then just add one when you're over what's 24 minus 10 well for a lot of people that's easier and you'll get 14 and then just add the one that you added to that originally and you'll end up with the same answer of 15 so always trying to figure out which way makes it easier for you to get the right answer let's try one more how about 42 minus 28 all right starting on the left what's 40 minus 20 you should get 20 right that's your running base total number 20 now we see that we have to borrow so just add that to the top what's 20 plus 2 22 and now we just minus the eight what's 22-8 22 minus 8 will give you 14 so as you can see all you're going to do when you do left-to-right subtraction is keep a running total in your head and just add it to the number if there's a borrowing situation that occurs go back into your workbook try the examples that we've got in the workbook go through and take your time make sure that you understand this process before you go any farther because borrowing is really a unique situation and when you have to do it if you can go left to right and just keep that running total in your head you'll have an estimated ID of the answer much easier in your head and you'll be able to get to the answer much quicker and faster give it a try and come right back after you're done [Music] okay how'd you do in the workbooks section of the two digit subtraction I hope you did great it's a little tricky but once you get used to it it's very easy and you can use it in any situation if you're still having trouble please go back and review the second part of this video and the exercises again in the workbook before you go into this part what I'm going to do now is some three digit subtraction without borrowing and then we're going to try one with and see how you do with this once you get into three digit numbers though it's a little bit more work to remember the base number you're working with so you've got to practice that a little bit alright let's try some easy stuff first how about 152 - 149 now you can see easily that's almost the same I just want to go through it left to right though to make sure you understand what we're doing what's 100 - 100 nothing left there's a zero there so you forget all about the hundreds now what's 50 minus 40 50 minus 40 should give you 10 so now you've got a 10 going on here's where you look there's a little borrowing here this number smaller than this so you got a 10 going let's bring it up to the 2 what's 10 + 2 12 and now subtract that 9 what's 12 minus 9 3 is the right answer so the answer this is 3 but I just want to show you how to keep it going left to right and keep the base numbers all right let's try another one 145 minus 132 starting on the left what's 100 minus 100 zero what's 30 - 30 10 is the answer to that so now we've got a 10 going again and now look at this this number is bigger than this number so you can go ahead and write that down and what's 5 minus 2 you should get 3 so the answer to 145 minus 132 is 13 all right let's try one more left to right how about 250 six - 150 - all right let's go over to the hundreds what's 200 - 100 you should get an answer of 100 and now come over here what's 50 - 50 0 so all you've got left so far is 100 that we had so let's go to the ones what's 6 minus 2 the answer is 4 so the answer total answer would be a hundred and four and if this is the cool part about subtraction as do it reverse and you'll see how easy it is to add remember how we add left to right go upside down adding what's 100 + 100 200 what's 0 + 5 5 and what's 4 + 2 6 always works if you get the right answer here you should be a little backwards and get the same answer up on the top now let me try one more with you that's going to bring you a little bit of borrowing but I want you to go through it slow because we're going to do a bunch of it let's do a 356 - 249 now it's sort of the left what's 300 - 200 we have a hundred going that's our base number what's 50 - 40 you should get Ted so now we've got 110 so far but here we go this is smaller than this so let's bring that 110 into the picture add it to the six so now you have 116 - the nine and if you got a - night it's easier to minus 10 and add one so what's 116 minus 9 well do the 100 16 minus 10 and you get 106 and then add the 1 back and you'll get 107 so let's look at it the other way 100 200 300 0 + 4 is not 5 but you can see here that you're going to carry one so what's 7 + 9 16 there's your six you're carrying the ones now this one and four is five so I'll add up backwards but when you carry what we have to borrow going left to right just remember to keep that base number on your head and then add it whenever you need to to the number as long as it's smaller than the number on the bottom try one more 423 - 369 all right let's give it a shot what's 100-400 - 300 you get 100 now look at this this is smaller than this 20 and 60 so this one's smaller so we're going to bring that hundred in so now 120 minus 60 is how much 120 minus 60 will give you 60 now we go to the next column look at this here we go again this is smaller than this we've got 60 going right so what's 60 plus 363 - the 9 remember 2 - 10 add 1 what 63 minus 10 just go down to 53 and then add the 1 back and you'll get 54 and if you do the reverse adding you'll see that you get the right answer again so now go into your workbooks and work on three digit subtraction and get used to adding that base number whenever you have to carry a bar and see how you do with that take your time make sure you understand it before you go on to the next section have a lot of fun [Music] all right now before we move on to the next chapter let's review a little bit about what we learned in the addition chapter just to make sure we've got that technique in our head okay I'm gonna give you a couple of examples to try first off question 245 + 124 remember we started on the Left we did 200 plus 100 and that gives us 300 and then we go to the next count that 4 is 4 tens or 40 so what's 300 plus 43 40 add 21 to that you should get 360 and then the next column 360 plus 5 is 365 and add 4 more and that will give us an answer of 369 all right now let's try another one but just a little bit bigger with a few more numbers in it how about a 215 134 and 325 same concept left to right just a few more numbers to put that base numbers to go down the columns starting at 200 and adding 100 you would get 300 AD 300 more and you'll have 600 now we go to the tens column select 10 right there what's 600 plus 10 610 ad 30 more and we'll get 640 and then add 20 to that so what's 640 plus 20 you should get 660 and now we're gonna go to the 1 what's 660 plus 5 665 add the 4 and it will get 669 and then add 5 more and you'll get 6 74 now just a little tip that hopefully you'll be able to use and learn on your own as you get through this program if you remember 200 300 600 610 640 660 now look over at the ones columns we're at 660 right isn't five and five ten so instead of going six sixty six sixty five like that six sixty notice groupings of tens and add them right to the base number so instead of the way we did it you could go 666 76 74 same answer just a little bit quicker and you'll find yourself doing that as you progress and practice this more and more let's try one more how about 353 217 321 and 218 all right starting left to right 400 plus 200 will give us 600 AD 300 more and we get 900 AD 200 more what's 900 plus 200 you should get 1,100 1,100 so now we've got a big number in our head 1,100 let's go to the next column that's a 50 what's 1100 plus 50 11 50 10 more is 11 60 20 more is 1180 and 10 more is eleven ninety and then we go to the next column look at this here's a 10 what's 11 90 plus 10 some people want to say 2,000 right away but it's actually 1211 90 plus 10 is is 1200 okay and then we come down here what's 1200 plus 1 is 1200 1 plus 8 more is 1209 the answer is 1209 so now go back through the workbook and review addition and subtraction make sure you understand them in a really confident because coming up next multiplication [Music] multiplication my personal favorite I'm going to show you a couple of different ways to multiply it all I want you to do is try each one out and see which technique makes the most sense to your brain the first one I'm going to teach you is called right-to-left cross multiplication sounds pretty difficult but it's very simple and all you do is actually write down the answer you'll eliminate all the stuff in the middle that you usually do and I'll show you how you don't used to do it and how you're going to do it just to try it okay easy example first is 14 times 12 now as I'm sure most people watching this have learned how to do to multiply these two numbers together you normally do 4 times 2 is 8 and then you do 1 times 2 is 2 and you put in your little zero down there and then 1 times 4 is 4 and then 1 times 1 is 1 and then you're going to add them all up you get eight six one and you get the answer using this technique it takes you one two three four five six seven eight steps nets without even a carry involved eight steps I'm going to show you how to do it in three very easy on what you do sprite down the same problem 14 times 12 three steps here's the three steps you do the right side you do a cross left play at and then you're the left side will go through it slow make sure you understand it first step is the right side just multiply the two numbers on the right what's four times two eight there's your first digit in the answer all right the second step is we're going to cross multiply when I say cross multiply I mean multiply these two numbers multiply these two numbers and then add them together so what's 2 times 1/2 and what's 1 times 4 4 so add them together what's 2 plus 4 you'll get 6 that's your second digit in the answer now to get the left digit just multiply the two numbers on the left what's 1 times 1 1 same answer 3 steps all this is gone you've already done it in your head along the way they said much easier much clearer and a lot of people that I mean have trouble with multiplication usually don't write that neatly in a of adding up the columns incorrectly that's where a lot of people make mistakes so this clears that right up let's try a couple more examples because it's very simple to do and no matter how big the numbers get all you do is write down the answer because as big as it can get is 9 times 9 so as long as you have your multiplication tables memorize you're in good shape let's try a 24 times 12 another pretty easy problem but I just want to show you how the technique works let's try the right side first remember 3 steps first step is the right side what's 4 times 2 8 there's the first digit of the answer to get the second digit and the answer all you have to do is cross multiply and add them together what's 2 times 2 4 what's 4 times 1 4 more so add them together what's 4 plus 4 8 there's your second digit the answer now to get the last digit the left digit just multiply the two numbers on the left what's 2 times 1 2 so your answer to 24 times 12 is 288 all right now if you have to carry in which in which case you will using right-to-left cross multiplication all you have to remember is that you carry it to the next step all right let's try this 24 times 13 3 steps first step is the right side what's the right side 4 times 3 what do you get 12 here's what you do you're right down the 2 from the 12 and you carry 1 where do you carry it to the next step so what I do is put a little one up in the top left corner alright because the second step is to cross multiply and then add right so just hang on to that for a second let's do the cross multiply what's 2 times 3 6 what's 4 times 1 4 so let's add them together what's 6 plus 4 10 that's our second step but remember we carried so let's add that one what's ten plus one we just get eleven so I'm going to write down one and once again I have to carry another wood so I put it over here and now I've got to do the third step which is the left side once two times one two and then we got to add the one we carry so what's two plus one is three so the answer is 312 it's that simple as hard as it gets is you have to remember to carry it to the next step if you have to carry it all let's try another one how about 36 times 24 all right three steps first step right side what's 6 times 4 24 write down the 4 carry the 2 we're going to carry to the next step the next step is the cross multiply and add let's cross multiply what's 6 times 2 12 what's 4 times 3 12 so now add them together what's 12 plus 12 you should get 24 and now we add that to that we carried so it's 24 plus 2 26 right down to 6 and we carry 2 let's carry the 2 over here now what's the last step the left side what's 3 times 2 6 add the 2 that we carried and you get 8 that's the answer the answer to 36 times 24 is 864 it's that simple let's just try one more how about 45 times 23 3 steps first step right side what's 5 times 3 15 I've wrote it right down to 5 and what do I carry the one I'm gonna carry the 1 to the next step which is the cross multiplying add let's cross multiply what's 5 times 2 10 what's 4 times 3 12 so add them together which 10 plus 12 now you're good at adding so you should have got 22 add the one we carried and they'll give you 23 I'm going to write down 2 3 and what am I going to carry to the next step 2 and now all I do is the left side what's 4 times 2 eight add the two and you get 10 1035 so the answer to 45 times 23 is 1035 look how neat that comes out you're still carrying but basically you're learning how to work with 110 and then hundreds by multiplying those groups together one step at a time now go to your workbook and take the time to go through all the exercises and really make sure you understand this technique because it's my favorite it's the easiest one and it works no matter what the numbers are all right so give it a try and we'll be right back [Music] I'm sure that that section was easy for you because right-to-left just makes so much sense and you get the answer right every time all you're going to do is know your multiplication tables and the three basic steps to getting the right answer so I hope you really enjoyed right-to-left cross multiplication but now I want you to try left-to-right cross multiplication same concept just a little bit backwards alright let me give it a try let's start with the same example I used in the previous section 14 times 12 now this technique is usually for people who are pretty good with numbers and like to work with numbers but give it a shot and see how you do instead of starting on the right here still a three-step process before we go backwards really start on the left all right so now here's the tricky part about left-to-right is you've got to know what every single number stands for that is a 10 that's a 10 that's a 2 and that's a 4 all right knowing that 3 starts going to the left side first and we're going to keep a running total so now we do the left side what's 10 times 10 100 you're right down 100 this is just keep a running total for you you really don't need to do this but just to show you how it works next step is to cross multiply and add what's 10 times 2 20 right add that to your base number so it's 100 plus 20 120 now the next step is the other cross what's 10 times 4 40 add that to your hundred 20 where do you get 160 and now the right side just won't apply the numbers on the right what's 4 times 2 8 edit to your 160 and there's one 6 meeting same technique except this time you want to keep a little bit of a running total in your head if you want to you can do it on paper but it's really easy to learn how to do and keeping in your head let's try another one same example we used earlier 24 times 12 first thing we do is we identify the numbers that's 20 that's 10 that's 2 for I don't know what each one stands for now the first step is the left side what's 20 times 10 20 times 10 and I'm sure everybody knows a shortcut to multiplying times 10 you just add a zero to the other number so if we have 20 times 10 just edit another zero to 20 and you should get 200 so we already have 200 now we have to do the second step which is that cross multiply what's 20 times 2 20 times 2 is 40 so we add that to our 200 and we get to 40 now we cross multiply the other way what's 10 times 4 40 what's 2 40 plus 40 more you should get to 8 and now the last step is the right side what's 4 times 2 8 so the answer is 288 this is a really simple technique but again it's for people who feel more comfortable with numbers so hopefully we've given us a try and what I'd like you to do now is go back into the workbook and go through the examples I put in there because if you practice this for a little bit just five or six examples you'll really see how easy this is and it's really not that hard you just got to practice keeping that running total that base number that's the hardest part but I'm sure you can do it [Music] now let's try complementary multiplication this is more of a little gimmicky multiplication and sort of gives you an advantage if the numbers are around 100 or 50 or 200 or a thousand but I just want to show you how it works because it's really fun and it makes a lot of sense to people and can be used for a great shortcut all right so let's try the first one numbers around 100 are really easy let's say you came up with a problem of 96 times 94 now we could use the way you'd learn how to multiply in school or we could use right-to-left cross multiplication to get the answer or we could use left-to-right cross multiplication get the answer but even easier and that's what I always do is whatever numbers you give me to multiply always try to pick the strategy that's easiest and most efficient for that problem so in this case I would use complimentary multiplication so here's how it works these are both relatively close to 100 so what I'm going to do is with the help our 96 way is from 100 how far away from 100 is 96 4 so let's put a third over here to the right now how far away is 94 from 106 so it's blue or 6 over here that's all you have to do now here's how you figure out what 96 times 94 is remember that's the goal all you do is you subtract diagonally that's the first step what's 96 minus 6 the answer is 90 and that's the first two digits in the answer to 96 times 94 now to get the second part of the answer all you have to do is multiply these two numbers on the right what's 4 times 6 24 put that right there and answer answer so the answer to 96 times 94 is 9024 that's simple and what's really neat about this is that you could subtract 96 minus 6 or you could subtract right away with 94 minus 4 now you either way you can get the same answer and then all you do is multiply the two numbers on the right and that's it let's try another one how about 97 times 95 first thing we do is we say okay how far away are those numbers from 100 well 97 is 3 away from 195 is 5 away from 100 so now all we have to do is subtract diagonal either way what's maybe 5 minus 3 or what's 97 minus 5 whichever one's easier for you you should use in this case I think 95 minus 3 is easier so 95 minus 3 gives me 92 there's the first two digits in the answer to get this what do we do multiply the two numbers on the right what's 3 times 5 15 so the answer to 97 times 95 is 9215 that's it it's that easy let's try another one but now remember when we were under 100 we subtracted diagonally so let me think would happen if we had two numbers are close to 100 but there are both over 100 assume 107 times 105 same concept except this time the numbers are over 100 instead of under 100 so when we were under 100 we subtracted diagonally in this case we're going to add because it's over 100 so how far over 100 is 107 7 and then how far over 100 is 105 5 so now we've got the problem set up and let's go through it first thing we do is we add diagonally the other way what's 107 plus 5 or 105 plus 7 either way you should get 112 and that's the first three digits and the answer now to get the last part of the answer just multiply the numbers on the right what's 7 times 5 35 so the answer is 11,000 235 now in the workbook here going to see where there's different examples that we do alone 50 around 200 around a thousand I want you to try them all if you have any trouble with this technique go back to another technique and get the right answer and then sort of make it like a puzzle let me give you an example if I said to you 196 times 194 all right now what do you think we should go from obviously these are both close to 200 so we're going up from 200 how far away is that from 200 196 is far away 194 is 6 away so the Buffalo 200 so we have to subtract first what's 196 minus 6 or 194 - for either will you do it it's going to come up to be 190 now you can write that down but you should because you've got to realize when we're working from 100 you don't touch it but when you're working from a different hundred you multiply it times that amount of hundreds so we're working from 200 s here so after you do the subtraction either way or addition then you have to multiply it times 2 because we're working with 200 so we came up with 190 so we got to double that times - what's 190 times 2 the answer is 380 and that's the first part of the answer to this equation now to get the last part simply multiply the numbers on the right what's 6 times 4 24 and if you check your math you'll see that 186 times 194 is 38,000 24 so many exercises if you have trouble getting to this answer use a different technique get the answer and then go backwards and see how could you get to that answer make it a puzzle that's all I did when I was a kid to learn how to do all these things and that's all I'm asking you to do is if it's a little bit tough for you make it a game I'm sure you'll get through it closing exercises get through it make sure you understand this it's a lot of fun and next we're gonna play something even more fun [Music] now I'd like to introduce you to box multiplication this technique is designed just to help people or if your child is having trouble organizing numbers through multiplication all right you can pick any size numbers and it works I'm just going to throw a couple of members out at random and show you how to set up the box and there's a very simple technique always getting the right answer and it does the organization of numbers at the same time it's really cool how it works let's take 32 while I'm going to put over here 14 32 times 16 all right now instead of doing any of the ways that I've shown you so far in this program I'm going to set up a little box here and the box is going to be split up into two by two like this because there's two two-digit numbers if it was two three-digit numbers you'd expand it out this way and draw a line or if it's four by three whatever just make the box accordingly alright but now we're doing 32 times 16 what I do is I put the numbers on top and on the side 32 times 16 then draw a line through each box diagonally to cut it in half and you can see how this cuts in half and this cuts enough now you have Kwolek and box 32 times 16 and all you have to do now is multiply the numbers into the box that they need at so let's start right here what's 2 times 1 the answer is 2 but now where do you put it in the box here's how it works the bottom right is for the 1 and this is for the tens the bottom is for the ones the top is when it's heads that's all you have to remember so 2 times 1 is 2 so the twos going to go in the bottom of the box all right now the next one is 2 times 6 is 12 so now you get 2 times 6 is 12 1 & 2 you draw it like this one goes to the top 2 those in the bottom there's your 12 that's your 10 that's your woods next is 3 times 1 3 times 1 is 3 Copperbottom where do you think it should go it should go in the bottom because it's just the ones and the last part is 3 times 6 3 times 6 is 18 so we draw it into the box 1 8 18 10 and 8 that's it now to get the answer here's all you have to do is just look at the numbers inside the box forget these are here now just look at the numbers inside the box and we're going to add them up diagonally it'll give you the answer right here all you have is a 2 so you put a little too here look at between these lines you have a 2 or one and an eight what's 2 plus 1 3 add eight more what do you get 11 you draw one and you carry one to the next line now I have these up in this one you see a 3 a 1 and a 1 what's 3 plus 1 plus 1 5 there's that and that's the answer 512 is the answer to 32 times 16 now going to your exercise workbook practice this a couple times with two digit numbers first then move up to 2 by 3 3 by 3 as high as you want to go but every time you'll see that it organizes your numbers and you always get an answer along the bottom give it a try [Music] now we're going to try squaring squaring a number just means that you're going to multiply a number times itself if I said to you 7 squared that just means 7 times 7 or 49 if I say 9 squared 9 times 9 would be 81 or even 12 squared 12 times 12 is 144 but most people tend to shut down after that and don't think they can multiply numbers any larger than that so we're going to show you right now and how to square larger numbers very quickly without doing that much multiplication let me give you a couple of examples just to show you how it works let's start with 96 squared 96 times 96 the average person can't even guess within a thousand of what that answer is going to be but using this technique I'm about to show you you'll be able to figure out the exact answer to this in a matter of seconds here's how it works 96 squared just look at 96 say okay how far away is 96 from 100 well the answer is 4 so all you do is you put a little minus or below it now what's 96 minus 4 the answer is 92 that is the first two digits of the answer to 96 times 96 now to get the last part of the answer all you do is you go to this middle the difference that was from 100 and you square that what's 4 times 4 4 times 4 not 4 plus 4 4 times 4 is 16 and just drop that below behind the 92 and that's the answer 9216 let's try another one how about 91 squared 91 squared 91 times 91 pretty difficult for using this it's really easy how far away is 91 from 109 so to prove little minus 9 here and what's 91 minus 9 if you have trouble with that do 91 minus 10 and then add 1 and either way you come up with 82 that's the first two digits in the answer 291 times 91 to get the last part what do we do you're going to square the in the middle what's 9 squared 9 times 9 is 81 and drop that behind me 82 in your answers 8281 very simple trick works all the time get some little trick here the farther you get away from 100 or 1,000 or 50 whatever you're using but it always works now what if I gave you 100 + 6 squared now same concept is complementary multiplication sort of this is close to 100 how far over 100 is it 6 so now when it was under 100 you see how we subtracted but when it's over 100 we're going to add so let's try this what's 106 + 6 the answer is 112 and now to get the last part of the answer just square that number in the middle what's 6 times 6 36 drop it down in the back and he answered 106 times 106 is 11,000 236 very simple practice this it's any workbook there's a bunch of exercises for it make sure you understand it but before you go to the workbook I want to show you a couple of certain examples that will help you understand this even better this is great if it's around 100 but what if it's not around 100 let's say for example the number you want to square is 46 so I'm going to do 46 squared now that's not even remotely close to 100 it's very far away but it's really close to 50 so what were to do is go from 50 how far away from 50 is that 4 so we're going to put a little brightest for year now what's 46 minus 4 42 but here's where the trick comes in we're going from 50 now we're not going from 100 isn't 50 half of 100 so when you get to this number here you've got to cut it in half that's the only trick so what's happened 42 you just look at it and figure it out what's half of 4 2 what's half of 2 1 so now you get 21 that's the first two digits in the answer to 46 times 46 and now to get through the answer just square the number in the middle what's 4 times 4 16 you bring it right down behind the 21 and there's your answer 2001 sixteen works for all kinds of numbers what if I gave you 988 squared obviously it's not even close to 100 but it is really close to a thousand isn't it how far away from a thousand is 988 the answer is 12 so I'm going to put a little minus 12 here what's 988 minus 12 the answer is and you go left to right of course is 976 that's the first three digits in the answer now to get the last part to square that number in the middle what's 12 times 12 144 so the answer to ninety eight times nine eighty eight is nine hundred seventy six thousand 144 so now go to your workbook there's all kinds of tricks and easier ways to square numbers so I want you to practice different types of numbers from 50 around 100 maybe 200 even up to a thousand and make sure you understand if it's below 100 or below the number you're using you subtract and if it's above you add give it a shot and come right back I want to teach you how to square numbers ending in five [Music] [Music] now let's try squaring numbers that end in five it's real easy takes two steps you can score any number that ends in five just got to do a little bit of multiplication and that's it let me give you an example 35 squared 35 times 35 really easy to do all this is two steps whenever this last number is five and then five the answer is always going to end in 25 that's a given always ends in 25 the hard part's getting the first part of the answer but it's really quite simple it's only one step just look at the first number here three all you do is add one which would give us a 4 and multiply those two numbers together what's 3 times 4 12 so the answer to 35 squared is 12 25 work 1225 let's try another one how about 65 squared ends and 5 so what's the answer going to end in 25 now how do we get that first part of the answer just add one to this first number what's one more than 6 should get set now multiply them together what's 6 times 7 42 so the answer is 42 25 or 4225 now try this one on your own first and then we'll do it together how about 85 squared try it out how's it do what's the first thing here ends in 5 so it ends in 25 one more than 8 is 9 ones 8 times 9 72 so the answer 72 25 or 7225 now this will even work with bigger numbers you just got to do a little more multiplication let me give you an example if I so view 995 squared 995 square 995 times 995 is a really big number but once again it ends in 5 so what's the answer going to end in 25 now to get that first part of the answer whatever is in front of this fine in this case 989 add one to it what's wrong more than 99 100 so now what's 99 times 100 what I do is whenever you multiply number times one hundred is add two zeroes so you'd have nine nine zero zero two five always works but when you get into bigger numbers you've got to really practice your multiplication again that goes back to the multiplication chapter so just for fun the next time your parents or your friends around you what impress them really fast just ask them to pick it over theirs and five and tell them you'll square just like that you'll beat them on the calculator now let's just review what we've learned so far in the previous sections just to make sure your brain still going and you remember all the little tricks and techniques that we've gone through starting out with addition remember how to add left to right I'm going to give you a couple of examples and I just want you to give them a shot 37 42 21 and 18 remember add left to right give it a shot okay now you should have started on the left this three is 30 because we're only working with two-digit numbers remember here's 40 so let's start a running total that base number what's thirty and forty seventy add 20 more 90 and how about ten more you're up to 100 already now let's go to the next column what's 100 plus seven 107 two more is 109 one more is 110 and eight more will give us 118 you should have got 118 all right and if you're still having trouble with this or if you forgot how to do it please go back to the first section of this program and practice your addition it's the most important thing you can learn in this program to make sure you can get through the rest of it now let's try one more but this time with three-digit numbers how about 257 322 and 214 go ahead and give it a shot that will try to get second okay let's go through it slow together okay starting here 200 we're working with hundreds first 200 and 300 will give us 500 AD 200 more 700 then we go up to the 50 what's 700 plus 57 50 plus 20 more is 77010 more is 780 and then we go to the ones what's 780 plus 7 787 and then 2 more would give us 789 and then 4 more would give us 793 so the answer 793 how'd you do if you have any troubles please go back to the addition section if not risk by some subtraction okay let's review subtraction out just a couple of quick examples to make sure you still remember how to subtract start off with 81-68 all right give it a try see how you do okay now let's try it together first you start over here what's 80 minus 60 you should have 20 and now you can see that this number is smaller than the number on the bottom so we have to borrow sort of so we bring this 20 up here makes it 21 right 21 minus 8 is how much 21 minus 8 and if you have trouble with that do 21 minus 10 and add 2 that's the same as subtracting 8 so you should get the answer of 13 all right let's try one more but a little bit bigger now let's do 426 - 219 okay starting from the left what's 400 minus 200 should get 200 keep in your head let's go over here what's 20 minus 10 10 so so far we have two hun and 10 right but here we go we see that this number is smaller than this number so we have 210 let's add it to the fix what's 210 plus 6 should get to 16 now minus 9 to 16 minus 9 forget all about the 200 for a second because you know that 200 is there and just do the 16 minus 9 you should get 7 and then bring the 200 back in and you should get the answer of 207 and just to make sure you're right remember you can always add backwards and upside down and get the right answer up on the top so if you have any troubles with subtraction please go back into the workbook and review that section if not good luck with the rest of the program [Music]
