in this video we're going to focus on mental math techniques so let's say if you want to add 34 plus 58 in your head how would you do it what's a quick and simple technique so what i like to do is i like to break down the numbers into small numbers 34 is basically 30 plus 4. 58 is 50 plus 8. now it's pretty much straightforward to add thirty and fifty you know that three plus five is eight so thirty and fifty adds up to eighty and then four plus eight is twelve eighty plus twelve is ninety two and so that's a simple way to add two numbers so let's try another example go ahead and add 69 and 45 so 69 we can write it as 60 plus 9 45 is 40 plus 5. now if we add 60 and 40 that's gonna be a hundred nine plus five is fourteen a hundred plus fourteen is one fourteen now let's try some examples involving three digit numbers go ahead and add 176 and 258 so 176 is 100 plus 70 plus 6. 258 is 200 plus 50 plus 8. so first let's begin by adding 100 and 200. so that's equal to 300. now if we add 70 and 50 how much is that well we know that 7 plus 5 is 12. so 70 plus 50 is 120. and what about 6 plus 8 6 plus 8 is just 14. now 120 plus 14 that's 134 and if we add 300 to 134 it's 434 and if you have a calculator with you you can add 176 plus 258 you should get 434 and of course it's always good to review the old techniques you can always add it by hand six plus eight is fourteen carry over the one one plus seven is eight plus five that's thirteen carry over the other one one plus one plus two is four so you can confirm your answer using that method as well here's another example 549 plus 678 feel free to pause the video and try that so 549 is 500 plus 40 plus 9. 678 is 600 plus 70 plus 8. so what's 500 plus 600 well we know five plus six is eleven so five hundred plus six hundred is eleven hundred or one thousand one hundred now what about forty and seventy four plus seven is eleven so forty and seventy is one ten and then finally we have nine plus eight which is a seventeen one ten plus seventeen is one hundred and twenty seven and if you add 127 to 100 that's 227 so 1100 plus 127 must be 1227 and so that's the final answer now let's try some examples involving subtraction what is 75 minus 38 so we can use the same technique we can break down 75 into 70 plus 5. and 38 is basically 30 and 8 but you need to apply the negative sign to both numbers not just a 30 otherwise it's not going to work so now 70 minus thirty that's equal to forty so we have forty plus five minus eight now five minus eight is a negative number that's going to be negative three and forty minus three is thirty 37 so 37 is your final answer now what about this 143 minus 56 go ahead and work on that example so we can write this as a hundred plus forty plus three and fifty six we can write that as fifty and six making both numbers negative now a hundred minus fifty there's many ways in which you could do this but let's do a hundred minus fifty because that's positive fifty and three minus six well that's going to be negative three you can do this in many different orders um so you just pick and choose whichever uh order you feel comfortable in doing this now 40 minus 3 is 37 and 80 plus 37 i mean 50 plus 37 is 87 so that's going to be your answer for this example let's work on an example with three digit numbers try that so let's break down 356 into 300 plus 50 plus six and negative 189 is going to be minus 100 minus 80 minus 9. so let's start with 300 minus 100 3 minus 1 is 2 so 300 minus 100 is 200 next we have 50 minus 80 which is negative 30 since 5 minus 8 is negative 3. and then we have 6 minus 9 which is negative 3. now two hundred minus thirty that is equal to a hundred and seventy and one seventy minus three that's going to be one sixty seven and so that should be the final answer now you can confirm it by subtracting these numbers by hand now six minus nine we can't subtract it it's a negative number so we need to borrow a one from the five so that's going to turn into a four we're going to carry over one to the six making it 16. 16 minus nine is seven now four minus eight is the negative number so we're gonna have to borrow another one making this two and making the four fourteen fourteen minus eight is six two minus one one so we get one sixty seven so you can confirm it using uh that technique now let's work on simple multiplication problems what is 5 times 4 so hopefully you've committed this memory you know your multiplication tables up to twelve but let's say if you don't know it what is five times four five times four is basically five added four times multiplication what it really is is repeat addition so five times four means you're adding five four times five plus five is ten the other two fives add up to ten ten plus ten is twenty so five times four is twenty you could also see it this way five times four and four times five are the same four times five means that you're adding four five times four plus four is eight the next two fours add up to eight and then we have one four remaining a plus eight is sixteen sixteen plus four is twenty so you get the same answer so let's say if we wanna find the value of six times five which is the same as five times six all we need to do is add six five times or add five six times whichever is easier six plus six is twelve so these two add up to twelve as well and twelve plus twelve is twenty four plus six that's thirty so six times five or five times six is thirty now what about eight times three this is simply eight plus eight plus eight three times eight plus eight is sixteen and what's sixteen plus eight well six plus eight is fourteen so think of 16 as 10 plus 6 plus 8 and if 6 plus 8 is 14 and 10 plus 14 is 24 then 8 times 3 is 24. now what about this example let's use two digit numbers instead what's 20 times 13 now sometimes it might be useful to think of math in terms of money so imagine if you have 13 20 bills what is the value of thirteen twenty dollar bills well you know the value of five twenties is a hundred another set of five twenties is another hundred so that's ten twenties you have so you have three twenties left over three twenties is sixty so at this point you've added thirteen twenties five plus five plus three is thirteen so if you add a hundred plus a hundred plus sixty you have two sixty so thirteen twenties equate to two hundred and sixty dollars another way in which you can get that same answer is you can break down 13 into 10 plus 3 and then use the distributive property 20 times 10 is 200 and 20 times 3 is 60. so 200 plus 60 gives you 260. so that's another way you can do it let's try another example what is 25 times 7 so imagine if you have seven quarters what is the value of seven quarters seven quarters is a buck seventy five therefore twenty five times seven is one seventy five now let's confirm it twenty five we could break it down into twenty plus five and now let's multiply by seven so what is seven times twenty well we know seven twenty dollar bills is a hundred forty dollars and seven times two is fourteen if you add the zero you're going to get 140 and then 7 times 5 is 35 so now if you want to add 140 plus 35 you could break it down like this 35 is 30 plus 5. 140 plus 30 is 170 and then add five you get 175. now what is 50 times 49 in this problem you don't want to find the value of 49 50 bills that's going to take some time to add that up instead what we want to do is replace 49 with 50 minus 1 and then distribute 50 times 50 how much is that well we know 5 times 5 is 25 all we got to do is add the two zeros so 50 times 50 is 2500 and then 50 times negative one that's negative 50. so 2500 minus 50 is 24.50 if you don't see this answer immediately you could break down 2500 into 2400 plus 100 and you know 100 minus 50 is 50. so therefore you're going to have 2400 plus 50 which is equal to 24.50 so that's 50 times 49. so what about this one what's 99 times 80 so based on the last example you know that the best way to do this is to rewrite 99 as 100 minus 1 and then multiply by 80. so 80 times 100 well 8 times 1 is eight and then all we gotta do is add the three zeros so this is going to be eight thousand and then eighty times one is eighty so what is eight thousand minus eighty well first eight thousand is seventy nine hundred plus a hundred and it's easy to do a hundred minus eighty that's twenty and then add twenty to seventy nine hundred so this is going to be seventy nine twenty now let's confirm this answer by using the old-fashioned multiplication technique so zero times nine is zero and that's also zero if we multiply these two numbers next we need to add a zero eight times nine is seventy-two carry over the seven and then this eight times nine is also 72 plus seven that's 79. so when you add this you get 79 20. let's try one more multiplication example 76 times 54 so what i like to do is break down 76 into 70 plus 6 and 54 into 50 plus 4. now we need to for you we need to multiply 70 times 50 7 times 5 is 35 and then add the two zeros next let's multiply seventy times four seven times four is twenty eight and then we just gotta add one zero and then we have six times fifty six times five is thirty and we gotta add a zero so six times fifty is three hundred if you have six fifty dollar bills that's three hundred dollars and then finally six times four is twenty four now we can add three hundred and two eighty that's going to be five eighty and 24 you can think of it as 20 plus 4. now 580 plus 20 that's going to be 600 and 3 500 plus 600 well 35 plus 6 is 41 so this is going to be 4100 and then plus 4 that's 4104 so that's how you can do it mentally but now let's confirm that answer by multiplying these two numbers so 6 times 4 is 24 carry over the 2 and then 7 times 4 is 28 plus 2 that's 30. now we need to add a zero 5 times 6 is 30 so we're going to add a 3 and then 5 times 7 is 35 plus 3 that's 38. now let's add four plus zero is four and zero plus zero is zero three plus eight is eleven carry over the one three plus one is four so we get the same answer four thousand one hundred and four now let's move on to division so let's say if we want to divide 324 by two how can we do so mentally so first divide 32 by two that is equal to sixteen and then divide four by two that's equal to two so it turns out that 324 divided by two if you type in your calculator you're going to get 162. so here's another example 168 divided by 4. notice that 16 and 8 are multiples of four so we can use that simple division trick so first let's divide sixteen by four sixteen divided by four is four next let's divide eight by four eight divided by four is two so this will give you forty two and it's always good to confirm your answer with the calculator just to make sure you're doing it correctly try this one 963 divided by three now we really don't have to do 9 96 divided by three because nine six and three individually are all multiples of three so first let's divide nine by three we could do it one at a time nine divided by three is three six divided by three is two and three divided by three is one so therefore this is three hundred and twenty one now what if we don't have a nice number for example let's say 156 divided by four 15 is not divisible by four and six is not either so what can we do in this example in a situation like this break down 156 into smaller numbers numbers that are divisible by four for example a hundred is divisible by four and 40 is divisible by 4 and 16 is divisible by 4. 40 plus 16 is 56 and 56 plus 100 is 156 so both sides of the equation are equivalent they're balanced they have the same value now how many times does four go into 100 you know four quarters is a dollar so 100 divided by 4 is 25 40 divided by 4 is 10. 16 divided by 4 is 4. now 25 plus 10 is 35 35 plus 4 is 39 so therefore 156 divided by 4 is 39 now you can confirm it using long division 4 goes into 15 three times 4 times 3 is 12. 15 minus 12 is 3 bring down the four goes into 36 nine times and so the remainder is zero so 156 divided by four is 39. now let's work on some more practice examples let's divide 234 by three so now you don't want to use 200 200 is not a multiple of three however you can use 210 because 3 goes into 21 so 3 will go into 210. and you also could use 24 because 24 is a multiple of three so you want to break down 234 into 210 and 24. you want to break it down into two numbers that are both divisible by 3. now we know that 21 divided by 3 is 7 so 210 divided by 3 is 70 and 24 divided by 3 is 8. so this is equal to 78. now let's confirm it using long division three goes into 23 seven times three times seven is twenty one twenty three minus twenty one is two bring down the four three times eight is twenty four so as you can see this is equal to seventy eight let's try another example 84 divided by seven so what two numbers should we break down 84 into what i would choose is 70 and 14 because they're both divisible by 7. seventy divided by seven is ten fourteen divided by seven is two ten plus two is twelve so eighty four divided by seven is twelve now what about one forty five divided by five so what we could do is break this down into a hundred plus forty plus five because each of these numbers are multiples of five a hundred divided by five is twenty because it takes five twenty dollar bills to make a hundred forty divided by five is eight five divided by five is one so this is going to add up to 29 and this is going to be the final example 168 divided by six so 60 is definitely a multiple of six so we can add another 60 so that's 120 so which means we have 48 left over 60 plus 60 plus 48 adds up to 168. 60 divided by 6 is 10 and 48 divided by 6 is 8. 10 plus 10 is 20 20 plus 8 is 28. so therefore 168 divided by 6 is 28. so those are some simple division tricks that you can use if you're dividing a big number by let's say a one digit number