Multiplying by 11
Date: 09/16/97 at 05:55:04 From: Benjamin Silbert Subject: A problem my class wants to know My teacher is a mathematician and one day she asked us to give her a number times 11. We said: 568 x 11, and after about 5 seconds she said the answer was 6248, so we checked on our calculators and she was right! We want to know how she does it so quickly!
Date: 10/31/97 at 11:37:11 From: Doctor Trent Subject: Re: A problem my class wants to know Multiply it out on paper, and you'll see that she's just adding digits: 568 x 11 ------- 568 568 ------- 6248 You can do it like this: in 568, 8 is the last digit, so 8 is the last digit in the answer. 6 is the second to last digit, so you add it to 8, and 6 + 8 = 14, so 4 is the tens digit; 5 and 6 are the first two digits of 568, and 5 + 6 = 11 (plus the carried 1 from before) = 12, so the next digit is 2 with 1 carried. 5 would be the first digit, but we add the carried one to get 6. With practice, you can do it in your head quite quickly. Here's a longer example to help put it together: 7348 x 11 8 is the last digit 4 + 8 = 12 2 is the tens digit, carry a 1 3 + 4 = 7 plus the carried 1 is 8, no carries 7 + 3 = 10 0 is the next digit, carry the 1 7 plus the carried 1 is 8, the first digit so: 7348 x 11 = 80828 -Doctor Trent, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 10/31/97 at 17:50:20 From: Benjamin Silbert Subject: Re: A problem my class wants to know Dr. Math, I asked my teacher and then my dad: My dad said: Multiply it by 10 and then add the number on. My teacher said: use 33 x 11 33 put down the first number (3) 3 add them together 6 put down the last number 3 and your total amount is 363. Benjamin Silbert
Date: 11/01/97 at 09:10:19 From: Doctor Sonya Subject: Re: A problem my class wants to know Dear Benjamin, Thanks for letting us know the other ways to do this problem. Your dad's seems to be the simplest, but could be difficult if the numbers were really big. For example, what if we wanted to find 674 x 11? We'd have to add 674 + 6740. I like your teacher's way best. Write us if you have any more questions. -Doctor Sonya, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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