Neat tips and math tricks part 1
Hey all you math geniuses out there, this is for you and today I'm going to show you some neat tricks and tips that can help you buzz through math problems, whether mental, numerical, theoretical or any other type. Stay tuned for parts 2 and maybe more!
#1 Tratchtenberg method
Derived by a Russian Jewish Nazi prisoner in world war II, this is a system of rapid mental calculations that allows oneself to compute mathematical problems in one's head quickly and accurately. This can be used for any operation, but I will teach you the general multiplication trick because it is most likely the most famous. For the other methods, look here. Let's take an example multiplication problem, starting simple. We'll begin with 64 * 57. What you do is
4*7 = 28, take the 8 and carry the 2, the 8 is the ones digit.
Now do 7*6 and 5*4. Add them together and you get 62. Add the 2 from the last equation brings it up to 64. Take the 4, that is your tens digit. Carry the 6.
Last step: do 5*6 = 30. Add the 6 and you get 36. Add that to the front of your answer and you get 3648! (Not a factorial). This also works for 3 digit and more numbers.
Still don't get it? Head on over to the "here" hyperlink to the Wikipedia article.
#2 Square root method
This is a very useful but not always completely accurate and is always accurate to the nearest tenth. So, let's start with the square root of 67.
Find the closest perfect square root below the number in this case, radical 64, meaning 8 and take the 8, double it , that is the denominator. The numerator is the number 67 minus the closest low perfect root 64, which is 3. So, you arrive at your answer. 8 3/16 or 8.1875, which is close to the real answer is around 8.1535. Another example is radical 88, which is 9 7/18 or 9.3889, and the real answer 9.3808. So, as you can see, this is a real useful method.
#3 Divisibility Rules
Divisible by 2 if the number's last digit is divisible by 2 (e.g. 298).
Divisible by 3 if the sum of the digits of the number are divisible by 3 (501 is because 5 + 0 + 1 equals 6, which is divisible by 3).
Divisible by 4 if the last two digits of the number are divisible by 4 (2,340 because 40 is a multiple of 4).
Divisible by 5 if the last digit is 0 or 5 (1,505).
Divisible by 6 if the rules of divisibility for 2 and 3 work for that number (408).
Divisibility by 7: More complex than it is to actually divide it, but here you go: take the last digit, which you call c, away from the number and call that number a. If a-2c is divisible by 7, then the number is divisible by 7.
Divisible by 9 if the sum of digits of the number are divisible by 9 (6,390 because 6 + 3 + 9 + 0 equals 18, which is divisible by 9).
Divisible by 11 if the sum and difference of alternating digits is divisible by 11, starting with minus. (e.g. 121 because 1-2+1 = 0 which is divisible by 11)
Divisible by 12 if the rules of divisibility for 3 and 4 work for that number (e.g. 408).
Again, stay tuned for part 2 for more tricks.
#1 Tratchtenberg method
Derived by a Russian Jewish Nazi prisoner in world war II, this is a system of rapid mental calculations that allows oneself to compute mathematical problems in one's head quickly and accurately. This can be used for any operation, but I will teach you the general multiplication trick because it is most likely the most famous. For the other methods, look here. Let's take an example multiplication problem, starting simple. We'll begin with 64 * 57. What you do is
4*7 = 28, take the 8 and carry the 2, the 8 is the ones digit.
Now do 7*6 and 5*4. Add them together and you get 62. Add the 2 from the last equation brings it up to 64. Take the 4, that is your tens digit. Carry the 6.
Last step: do 5*6 = 30. Add the 6 and you get 36. Add that to the front of your answer and you get 3648! (Not a factorial). This also works for 3 digit and more numbers.
Still don't get it? Head on over to the "here" hyperlink to the Wikipedia article.
#2 Square root method
This is a very useful but not always completely accurate and is always accurate to the nearest tenth. So, let's start with the square root of 67.
Find the closest perfect square root below the number in this case, radical 64, meaning 8 and take the 8, double it , that is the denominator. The numerator is the number 67 minus the closest low perfect root 64, which is 3. So, you arrive at your answer. 8 3/16 or 8.1875, which is close to the real answer is around 8.1535. Another example is radical 88, which is 9 7/18 or 9.3889, and the real answer 9.3808. So, as you can see, this is a real useful method.
#3 Divisibility Rules
Divisible by 2 if the number's last digit is divisible by 2 (e.g. 298).
Divisible by 3 if the sum of the digits of the number are divisible by 3 (501 is because 5 + 0 + 1 equals 6, which is divisible by 3).
Divisible by 4 if the last two digits of the number are divisible by 4 (2,340 because 40 is a multiple of 4).
Divisible by 5 if the last digit is 0 or 5 (1,505).
Divisible by 6 if the rules of divisibility for 2 and 3 work for that number (408).
Divisibility by 7: More complex than it is to actually divide it, but here you go: take the last digit, which you call c, away from the number and call that number a. If a-2c is divisible by 7, then the number is divisible by 7.
Divisible by 9 if the sum of digits of the number are divisible by 9 (6,390 because 6 + 3 + 9 + 0 equals 18, which is divisible by 9).
Divisible by 11 if the sum and difference of alternating digits is divisible by 11, starting with minus. (e.g. 121 because 1-2+1 = 0 which is divisible by 11)
Divisible by 12 if the rules of divisibility for 3 and 4 work for that number (e.g. 408).
Again, stay tuned for part 2 for more tricks.
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