ADDITION FROM LEFT TO RIGHT:-
Let's start with an example:- 78 + 45 = ?
STEP - 1. We start adding left to right. 7+4 = 11. We keep this figure in our heads.
STEP - 2.- We now add 8 and 5 which equals 13. Remember that these steps are absolutely mental. Here you say to yourself, 11 and 13. Our sum now looks like this:-
STEP - 3. In our final step, we 'combine' or add the middle digit of the two figures as shown by the arrow. This step is completely mental. So our answer becomes 123.
Example No. 2.
87+69 =?
STEP - 1. We add mentally 8+6 = 14. We hold the figure 14 in our mind.
STEP - 2. Now we add 7+9 = 16.
STEP - 3. In the final step, we will add or 'combine' the middle digits 4 and 1 in our minds. So our answer becomes 156.
Example:- 3. 48 + 97 = ?
STEP-1. We add 4 + 9 = 13. Keep this figure in your mind.
STEP:-2. Now we add 8+7 = 15.
STEP:-3. In the final step, we add the middle digit and the final answer looks like this.
Left To Right Addition:-
The method which we just learned can be applied to three-digit and four-digit problems as well.
Example-1. 582 + 759 = ?
STEP:-1. We start solving the sum by adding the digit in the first column. We add 5 + 7 = 12 and we keep the figure in our mind. Our sum now looks like this.
STEP-2. We now add the digits in the middle column. We add 8 + 5 = 13. We now have two figures in our minds 12, 13. We will now combine and add the middle digits just like in the case of two-digit addition. So we have 133 in our mind now, after adding the middle digits.
STEP-3. In our final step, we add 2 + 9 in the final column. We get 11. We will combine 133 and 11. The answer will be right in front of us as 1341.
This method is new and can be done mentally as I showed here. With a little bit of practice, you will be fine.
Example-2. 983 + 694 = ?
STEP-1. Here we add the first column digits from left to right. 9 + 6 =15. We keep this figure 15 in our mind.
STEP-2. Now we add the digits of the middle column, 8+9 = 17. We combine 15, 17 giving us 167. Our sum now looks like this.
STEP-3. We add the last column, 3 + 4 =7. We already have 167 in our mind and we bring down 7 making the answer 1677. There is no need to combine here as a 7 is a single digit. So our answer is 1677.
Let's now do some difficult addition sums using this method.
Que.1. 5273 + 7372 + 6371 + 9782 = ?
STEP-1. This sum is to be done exactly the same way we have learned in this chapter. We move column by column from left to right. Here we add 5 + 7 + 6 + 9 = 27.
We keep 27 in our minds and move on to the next column.
STEP-2. We add the second column 2 + 3 + 3 + 7 = 15. We now combine 27 from the first column to 15 from this column. This gives us 285. Our sum looks like this now.
STEP-3. We will now move on to totaling the third column 7 + 7 + 7 + 8 = 29.
In our minds, we already have 285. So we now combine 285, 29. So this gives us 2879. Our sum now looks like this.
STEP-4. In our final step, we total up the final column. We get 3 + 2 + 1 + 2 = 8. Now, because 8 is a single digit, we simply just bring it down. So our answer becomes 28798.
Que.2. 8336 + 4283 + 3428 + 9373 = ?
STEP- 1. Just like before we add 8 + 4 + 3 + 9 = 24 from the first column. We keep this in our minds.
STEP-2. We add the second column from the left, 3 + 2 + 4 + 3 = 12. We now combine and add. So we have 24, 12. We get 252, which we keep in our minds for a while.
STEP-3. We take the third column and add the digits in it, 3 + 8 + 2 + 7 = 20. We combine and we get 2540 like this.
STEP-4. In our final step, we add the digits in the Rightmost column. 6 + 3 + 8 + 3 = 20. We get 20 and we combine it with 2540. So we have 2540, 20 giving us 25420 as our answer. The sum looks like this.
Example-1.
24 + 9 = ?
Solving this is actually quite easy if you apply the math sutra " By Addition And By Subtraction".
See 9 is very close to 10 and they differ by 1 only. So if we add 10 to 24, which is quite easy to do, and then subtract 1 from the total, which is also very simple to do. We can then arrive at our answer. The sum looks like this.
Example:-2
56 + 8 = ?
We apply the same rules here as well. 8 is very close to 10. We can add to 10 to 56 and take away 2 to arrive at our answer.
I hope it is clear as to why we take away 2, after adding 10.
Example:-3.
46 + 18 = ?
Here we add 20 to 46 making it 66 and then subtracting 2, giving us 64 as our answer figure.
Example:- 4.
168 + 19 = ?
Here we add 20 to 168 to making it 188 and then subtracting 1, giving us 187 as our answer figure.
Example:- 5.
458 + 38 = ?
Here we add 40 to 458 making it 498 and then subtracting 2, giving us 496 as our answer figure.
