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Is there any technique to permanently remember multiplication/times table of numbers greater than 12 but smaller than 21?

For example, 13x1 = 13 .....through..... 20x10 = 200 ?

3 Answers3

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You could also work in terms of $(5a + b)(5c + d) = 25ac + 5(ad + bc) + bd$. None of the variables here gets bigger than 5, and 5 times large numbers is easy to calculate.

NovaDenizen
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$13\cdot1=13,20\cdot10=200$

In general nothing happens when you multiply by 1. Also muliplying by 10 just adds a zero at the end.

For everything else just memorize them the same way from 1 to 10. Also: remember multiplication is commutative.You might also want to try using base 20.

Asinomás
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Multiply and add their unit digits respectively, the unit digit of the required result is the same as the unit digit of the above product, the tens digit of the required result is the tens digit of the above product added to the above sum and hundred digit is 1 added to the tens digit of the tens digit. It holds for all numbers between 10 and 19. e.g $14\cdot17$ , $4+7=11$, $4\cdot7=28$, so the required result is 238 proof: let $x$ and $y$ be numbers between 10 and 19, then, $$x\cdot y=(x-10+10)\cdot(y-10+10)\\=x'\cdot y'+10(x'+y')+100\\=1(x'+y')x'y',$$ where $x'=x-10$ which is also the unit digit of x.

MJD
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Adokwu Ondoma
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  • Do you mean to get $23$ you multiply the sum by the tens digit and then add $1$? i.e. $(11\times2) + 1 = 23$ as opposed to what your saying which is $(11+2)+1 = 14$... – Zhoe Dec 27 '13 at 22:14
  • ...review my answer, the result follows from my proof, you have 1(11)(28), 2 leaving the first bracket to the second, you add, 1(11+2)8, i.e 1(13)8, the 1 from the bracket then adds up to the first term, (1+1)38 or 238, in each case, you should transfer the tens digit by adding to the nearest term on the left. – Adokwu Ondoma Dec 27 '13 at 22:44
  • Multiply and add their unit digits respectively $4\cdot7=28, \space 7+4=11$. The unit digit of the required result is the same as the unit digit of the above product: since the product was $28$, then the unit digit of the answer is $8$. Okay. The tens digit of the required result is the tens digit of the above product added to the above sum: the tens digit of the above product is $2$, added to the sum: 2+11 =13...the tens digit of $13$, is $1$??? And hundred digit is 1 added to the tens digit of the tens digit: also ??? This is confusing and doesn't follow the above comment. – Zhoe Dec 27 '13 at 23:16
  • For example, 154 is a three digit number, counting from left to right, the first digit 1, is called the "hundred digit", the next digit 5, is called the "tens digit", the following 4, is called the "unit digit". – Adokwu Ondoma Dec 27 '13 at 23:50
  • I am aware of that, I am just saying that if I followed your explanation I wouldn't arrive at the correct answer..Nowhere in your explanation does it say to write it as "$1(11)(28)$".. – Zhoe Dec 27 '13 at 23:56