Easy Method for Table of Numbers Ending With 9

H.D. Motiramani

Let us take Multiplication table of 19 first

19×1  =   1   9     =        19

19×2  =   3   8     =        38

19×3  =   5   7     =        57

19×4  =   7   6     =        76

19×5  =   9   5     =        95

19×6  = 11   4     =     114

19×7  = 13   3     =     133

19×8  = 15   2     =     152

19×9  = 17   1     =     171

19×10= 19   0     =     190

Here 19 is the multiplicand, 1 to 10 is called multiplier and the answer on right hand side is called product.

Observe that right hand side answers are split in two parts. This has been done deliberately to show that the First part from top starts with one for 19×1 and as we move downwards, it increases to next higher odd number like 1,3,5,7,…. 15,17,19.  In other words, it is a series of odd numbers.

Second part of product (answer) is also interesting. It starts from zero in the bottom and as we go up, it increases by 1 to become 0,1,2,3,4…7,8,9.

Thus the multiplication table of 19 shows peculiar characteristics.

Let us pay little more attention to the table of 19. Please note that the first part is the double of multiplier minus one . For example if multiplier is 6, than the first part is 6×2-1=11, and if the multiplier is say 9 then the first part of the answer is 9×2-1=17. Also, the right hand part in red color is nothing but ten minus multiplier. For example if multiplier is 7 then the second part of answer or red colored answer will be 10-7=3 and if the multiplier is 6 than the second part of the product/answer is 10-6=4. It therefore becomes quite easy to understand the process and do the calculation in our minds.

Another easy method of arriving at the result is by multiplying with 20 instead of 19 and then adjusting it by deducting the multiplier. For example 19×7 can be attempted as 20×7-7=140-7=133.

As a matter of fact such a practice of taking the multiplicand(that is the number ending with 9) to a next higher digit and then do the maneuvering by deducting the multiplier to get the answer. This practice holds good for all multiplicands whose last digit ends with 9.

For example 39×7 can be attempted as 40×7-7=280-7=273.

79×8 can be done as 80×8-8=640-8=632

Some more examples:

19×5=20×5-5=95

69×5=70×5-5=345

89×6=90×6-6=540-6=534

499×7=500×7-7=3500-7=3493

789×2=790×2-2=1580-2=1578

So, remember the formula: Increase the multiplier (ending with nine) by 1. Adjust the product by deducting the multiplier.

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