10 Math Tricks School Didn’t Teach You But Should Have
If you need to multiply some number from 1 to 10 by 9 you don't need anything but your hands place both palms before you and assign each finger a number just like shown on the screen if you need to multiply 3 by nine bend finger number three on the right you still have seven unbent fingers that's.
The first part of the answer on the left only two fingers are left unbent and that's your second part voila nine times three equals twenty-seven well in the previous example we could only multiply the first ten digits by nine now we'll do this trick with just about any number and it's easy as pie take any random large number like one.
Thousand two hundred and fifty multiplying it by nine in a conventional way without a calculator would take you some time to make it simpler just add a zero at the end and subtract the original number that makes it twelve thousand five hundred minus one thousand two hundred and fifty and equals eleven thousand two.
Hundred and fifty that's how quick it is now let's take it a step further and learn to multiply any large numbers between each other for this we'll use a method taught in japanese schools let's take 12 multiplied by 31 as an example in this method the numbers multiplied are represented by tens and ones twelve will be one ten and two ones.
And thirty one will be three tens and a one now take a piece of paper and some colored pencils ideally four we'll draw the numbers making them visual first draw one diagonal line left to right going up it will represent 10 in 12. take another pencil and leave a gap below draw two more diagonal lines.
In parallel to the first one this is our 12. for number 31 we'll draw some more diagonal lines only these ones will go in the opposite direction and cross our original lines so it's three lines left to right going down for three tens and one more line with a gap above the first three for a.
One don't forget to use differently colored pencils as well to avoid confusion while you're still not used to this method now you have a diamond shape made of intersecting lines to calculate the result count the times all the lines cross each other at each corner of the diamond and write down those numbers at.
Each intersection you should have three at the left corner of the diamond two at the right corner one at the top and six at the bottom leaving the side corners alone for now add the top and bottom values together that'll be seven and if you now divide the diamond shape into three parts with vertical lines you'll get your desired.
Result 372. there's a catch though if you're trying to do it with numbers ending with five ones or more you might get double-digit results when counting the intersections so let's see how to deal with those taking 25 multiplied by 37 as an example so we draw two diagonal lines for two.
Tens and five more for five ones that's 25 for us now there are three crossing lines for three tens and seven more for seven ones and there's our thirty-seven now we count the dots six at the left corner of the diamond 35 at the right corner the times table will help you out a lot here to make it quick just multiply 5 by.
7. 14 at the top and 15 at the bottom a lot of double digit numbers here first let's add the top and bottom results as we did last time 14 plus 15 equals 29. now we have 6 29 and 35 take the rightmost number and only leave the 5 in it transferring the 3 to the middle number and adding it to the sum you'll get 6 32 and 5. do the same with.
32 now only leave the 2 and transfer the 3 to the left add it to the 6 and voila you've got your answer check yourself with the calculator if you want but 925 really is the correct result and finally the same method can be applied to even larger three-digit numbers let's take 322 multiplied by 14.
As an example first we draw 322 just as we did previously only now the hundreds are a separate set of diagonal lines there will be three two and another two next add the crossing lines of fourteen one and four you can see now we have not three but four sections so let's count the dots.
That's three in the leftmost section twelve at the first top eight at the second top two and two at the first and second bottom intersections and eight in the right most section adding the first top and bottom dots we get fourteen and adding the second ones we get ten and the result is 3 14 10 and 8.
And now you already know what to do transfer the 1 from 10 left add it to 14 then transfer the 1 from the resulting 15 left two and here you go four thousand five hundred and eight is your answer the multiplication table ends with ten and most people end up memorizing it.
Sooner or later but there's also a way to take it a step further and learn to multiply by 11 just as quickly let's take 34 as an example and multiply it by 11. first separate the digits making it 3 and 4 with a space between them in that space put the sum of these two digits three plus four equals seven.
That's your answer three hundred and seventy four with some numbers addition may result in a two digit number that's the case with say 87 you'll get 8 15 and 7. to get your actual result add the first digit and the tens place of the sum leaving the ones alone that will be 8 plus one.
Five and seven which results in nine fifty seven if you know the multiplication table well enough finding out percentages will be a piece of cake the only downside of the following method is that it can only be used with round percentages of round numbers but hey that's already something.
So if you want to find out 30 of 80 you just need to ditch the zeros and multiply the tens places of these two numbers three multiplied by eight will be twenty four same can be done with any rounded percentages and numbers sixty percent of thirty will be six multiplied by three equaling eighteen.
now let's get back to simple multiplication again we've covered multiplying by 11 but what about 15 let's try it with multiplying 64 by 15. first add a zero to the first number making it six hundred and forty now divide it by two resulting in three hundred and twenty and next add the two.
Numbers you've got six forty plus three twenty equals nine sixty you can verify it using the calculator but the principle is easy to grasp you first multiply your number by ten then multiply it by five which is half of ten get it and add those numbers a similar method applies to multiplying.
Any number by 20 30 or any other round number let's say you want to multiply 41 by 30. first add a zero to your number making it 410 now multiply it by 3 and you'll get 1 230. in fact multiplication basically boils down to a number of additions performed.
In a row let's try multiplying 16 by nine sixteen is two times eight which converts our task into two times eight times nine since eight times nine will be seventy-two we just need to add seventy-two with another seventy-two which gives us 144 let's take it up a notch and multiply.
Two digit numbers between each other say eighteen times twelve we can unfold these two numbers as two times nine and two times six next multiply nine and six resulting in two times two times fifty four one step further and we get two times one hundred and eight which leaves us with two hundred 216.
subtracting can also be a headache with large numbers but there's a simple trick to subtract any three-digit number from 1000 let's take 578 as an example what you need to do is subtract the first digit from nine nine minus five equals four now subtract the second digit from nine as well.
Nine minus seven is two and finally subtract the third digit from ten ten minus 8 gets you 2. now place your results together 422 is your answer the number of pi is infinite and the digits after the point go in a seemingly random order but there's a simple.
Technique to memorize the first six of them say the phrase how i wish i could calculate pi out loud or write it down now count the letters in each of the words and you'll get the three and the first six digits after the decimal 3.141592 you can multiply large numbers between.
Each other in your head easily but take note that this trick only works with numbers in the 90s so let's say you want to multiply 93 by 96 subtract either number from 100 getting you 7 and 4. now add the two results getting 11 and subtract it from 100 again receiving 89. this is the first part of your answer.
For the second part multiply these two numbers instead of adding them 7 times 4 equals 28 put it next to 89 and your answer is just that 8928.