Single digit subtractions

Remembrance of subtraction of a single digit from a single digit or from the numbers such as 10, 11, 12, ----17, 18 is necessary beside   the single digit additions.

0  -  0  =  0 1   -  0  =  1 1   -  1  =  0 2  -  0  =  2 2  -  1  =  1 2  -  2  =  0 3  -  0  =  3 3  -  1  =  2 3  -  2  =  1 3  -  3  =  0 4  -  0  =  4 4  -  1  =  3 4  -  2  =  2 4  -  3  =  1 4  -  4  =  0 5  -  0  =  5 5  -  1  =  4 5  -  2  =  3 5  -  3  =  2 5  -  4  =  1 5  -  5  =  0 6  -  0  =  6 6  -  1  =  5 6  -  2  =  4 6  -  3  =  3 6  -  4  =  2 6  -  5  =  1 6  -  6  =  0 7  -  0  =  7 7  -  1  =  6 7  -  2  =  5 7  -  3  =  4 7  -  4  =  3 7  -  5  =  2 7  -  6  =  1 7  -  7  =  0 8  -  0  =  8 8  -  1  =  7 8  -  2  =  6 8  -  3  =  5 8  -  4  =  4 8  -  5  =  3 8  -  6  =  2 8  -  7  =  1 8  -  8  =  0 9  -  0  =  9 9  -  1  =  8 9  -  2  =  7 9  -  3  =  6 9  -  4  =  5 9  -  5  =  4 9  -  6  =  3 9  -  7  =  2 9  -  8  =  1 9  -  9  =  0

Due to the necessity of borrowing 1 from the previous  place, which is ten times of the respective current place, situations such as subtraction of 18 - d, 17 - d, ---, 11 - d and 10 - d arise. 
When at the place in the upper number is 8 and below that is 9 to be subtracted, then we have to borrow 1 making it 18, and the subtraction becomes as 18 - 9, naturally we need not think much, we must recollect 18 - 9 = 9. 
Similarly, when at the place in the upper number is 7 and below that is either 9 or 8 to be subtracted, then we have to borrow 1, making the subtraction as 17 - 9 or 17 - 8, we must be able to get instantly:  17 - 9 = 8 or 17 - 8 = 9; and so on. 

18  -  9  =  9 17  -  9  =  8 17  -  8  =  9 16  -  9  =  7 16  -  8  =  8 16  -  7  =  9 15  -  9  =  6 15  -  8  =  7 15  -  7  =  8 15  -  6  =  9 14  -  9  =  5 14  -  8  =  6 14  -  7  =  7 14  -  6  =  8 14  -  5  =  9 13  -  9  =  4 13  -  8  =  5 13  -  7  =  6 13  -  6  =  7 13  -  5  =  8 13  -  4  =  9 12  -  9  =  3 12  -  8  =  4 12  -  7  =  5 12  -  6  =  6 12  -  5  =  7 12  -  4  =  8 12  -  3  =  9 11  -  9  =  2 11  -  8  =  3 11  -  7  =  4 11  -  6  =  5 11  -  5  =  6 11  -  4  =  7 11  -  3  =  8 11  -  2  =  9 10  -  9  =  1 10  -  8  =  2 10  -  7  =  3 10  -  6  =  4 10  -  5  =  5 10  -  4  =  6 10  -  3  =  7 10  -  2  =  8 10  -  1  =  9

These subtractions are easy. However, one must read repeatedly, try to recollect and use in solving exercises involving these subtractions; without the use of any electronic device, and have practice to attain the best speed.

Mathematics was easy for me because

When I discussed with many 10^th standard students who find mathematics very difficult; I realized why mathematics was easy for me. The difference is that when I was a 4^th standard student most of my classmates were able to tell instantly; 29 x 9 = 261. However, these students who find mathematics hard cannot tell immediately 9 x 9 = 81 or even 9 + 7 = 16. Negligence to master the number operations such as addition, subtraction, division, multiplication at the proper time i.e. the primary school level is the main cause of poor performance of a student at the high school. One should be conversant with these operations and multiplication tables.

Everybody cannot be a mathematics wizard; but can use his ability to the maximum extent. Not only for the competitive examinations, but in general this quality is essential, even for the day to day study. This requires practice from the childhood. Availability of computers, electronic calculators, mobile phones and calculators therein is making many students unaware of the fact that these things are to be done mentally and that too at the greatest speed.

Primary and middle school days are the best to develop this ability. If you missed the days, you can do it at any advanced stage. It requires awareness. Once you decide, you can put some hard work. Repeated reading of the tables of multiplication from two ones are two to thirty tens are three hundred; squares up to 30; cubes up to 10; about 110 one digit additions and 55 one digit subtractions and 55 subtractions of one digit from the two digit numbers; such as 10 to 18. Additionally, practice of solving exercises is a must. Don’t forget to do it mentally.

There is no alternative to above things. It’s easy, provided you are determined to do it. Short cuts in arithmetic may be under different names such as Vedic mathematics, Abacus are additional; and will not help as alternative to the primary study of addition, subtraction, division, multiplication and multiplication tables.

For convenience, I reproduce the above mentioned tables, and few practice exercises in the following posts. Learn and practice with patience. These things look easy, but need a great devotion and ambition to learn by heart. It’s not the Aladdin’s lamp.  If you are a beginner, it may require months’ devotion, repeated reading, recollection and practice of solving addition, subtraction, and division and multiplication exercises. One day you will find mathematics easy and interesting.

Single digit addition

First step and essential requirement of education in any field is single digit additions at the tip of tongue. For convenience, I am listing herewith. Most of the combinations are covered and care is taken to minimize the unnecessary repetitions.

0  +  0  =  0        0  +  0  =  0 0  +  1  =  1        1  +  0  =  1 1  +  1  =  2        1  +  1  =  2 2  +  1  =  3        1  +  2  =  3 3  +  1  =  4        1  +  3  =  4 4  +  1  =  5        1  +  4  =  5 5  +  1  =  6        1  +  5  =  6 6  +  1  =  7        1  +  6  =  7 7  +  1  =  8        1  +  7  =  8 8  +  1  =  9        1  +  8  =  9 9  +  1  =  10      1  +  9  =  10

0  +  2  =  2        2  +  0  =  2 2  +  2  =  4        2  +  2  =  4 3  +  2  =  5        2  +  3  =  5 4  +  2  =  6        2  +  4  =  6 5  +  2  =  7        2  +  5  =  7 6  +  2  =  8        2  +  6  =  8 7  +  2  =  9        2  +  7  =  9 8  +  2  =  10      2  +  8  =  10 9  +  2  =  11      2  +  9  =  11

0  +  3  =  3        3  +  0  =  3 3  +  3  =  6        3  +  3  =  6 4  +  3  =  7        3  +  4  =  7 5  +  3  =  8        3  +  5  =  8 6  +  3  =  9        3  +  6  =  9 7  +  3  =  10      3  +  7  =  10 8  +  3  =  11      3  +  8  =  11 9  +  3  =  12      3  +  9  =  12

0  +  4  =  4        4  +  0  =  4 4  +  4  =  8        4  +  4  =  8 5  +  4  =  9        4  +  5  =  9 6  +  4  =  10      4  +  6  =  10 7  +  4  =  11      4  +  7  =  11 8  +  4  =  12      4  +  8  =  12 9  +  4  =  13      4  +  9  =  13

0  +  5  =  5        5  +  0  =  5 5  +  5  =  10      5  +  5  =  10 6  +  5  =  11      5  +  6  =  11 7  +  5  =  12      5  +  7  =  12 8  +  5  =  13      5  +  8  =  13 9  +  5  =  14      5  +  9  =  14

0  +  6  =  6        6  +  0  =  6 6  +  6  =  12      6  +  6  =  12 7  +  6  =  13      6  +  7  =  13 8  +  6  =  14      6  +  8  =  14 9  +  6  =  15      6  +  9  =  15

0  +  7  =  7        7  +  0  =  7 7  +  7  =  14      7  +  7  =  14 8  +  7  =  15      7  +  8  =  15 9  +  7  =  16      7  +  9  =  16

  

0  +  8  =  8        8  +  0  =  8 8  +  8  =  16      8  +  8  =  16 9  +  8  =  17      8  +  9  =  17

0  +  9  =  9        9  +  0  =  9 9  +  9  =  18      9  +  9  =  18

These additions look easy. One must read repeatedly, try to recollect and use in solving exercises involving additions without the use of any electronic device, and have practice to attain the best speed.