Strategy 2: Addition and Subtraction
Addition is the most basic arithmetic skill we all need to know. It is a key to all math calculations. Getting these new addition strategies right will make all other math strategies easier to learn, especially in multiplication, which you can learn once you decide to subscribe for this course.
What we have been taught in school is to align the numbers top to bottom, and then add from right to left; adding the ones digits first, carry over to the tens, then to the hundreds, and so on. While the conventional method may assure the most accuracy on paper, it isn’t the most natural approach to mental arithmetic, as we have been taught to read from left to right.
Anyone can testify to that. How many times have you been stuck up with carrying over sums to the next digit place, and then totally forgetting what your working sum figure is?
Our math strategy here is to focus on calculating from left to right, creating base numbers to remember the results easily. Understandably, you’ll start slow, but you’ll pick up speed the more you practice it.
Take these numbers for example:
529
183
+ 246
------
The underlined digits represent the hundreds place. Let’s start working there. Add 5, 1, and 2 together, and you’ll have 8. Since this is the hundreds place, your base number will be 800. It’s easier to remember the largest possible figure of a given equation if you tackle the leftmost digits. Try to fix that in your head.
529
183
+ 246
------
8 x x
Next are those digits in the tens place. Add 2, 8, and 4, and you’ll have 14. Since we have a carry-figure (1), let’s add that to our base figure 800, to make it 900. Therefore, we already have 900 and 40 to work with.
529
183
+ 246
------
8 14 x
9 4 x
Lastly, we tackle the digits in the ones place. We have 9, 3, and 6 to be added together, giving us a total of 18. Carry the 1 over to our previous result “40”, so we’ll have 50, leaving “8” for the ones place.
529
183
+ 246
------
9 4 18
9 5 8
The entire equation will yield a total of 958.
You see, the key to making this work easy is to keep the base number in your head at all times. In Vedic arithmetic, this is called “on the flag” approach, because you are shoring up the base number in your head and manipulating it mentally with subsequent results.
This method is extremely handy when calculating rough estimates of everyday business figures. Simply getting the leftmost numbers right through mental math will make you blurt out the answer way faster than your colleagues!
Try it out with the following few examples below. With this method, you don’t need to write your step-by-step equations on a piece of paper. It may seem slow at first for you, but what can we expect from reprogramming your brain to take on a new path? Keep honing your skills using this approach and mental addition will be a cinch for you!
Addition Practice
826 557 292 981 829
493 963 377 357 717
+ 279 + 181 + 426 + 622 + 234
------ ------ ------ ------ ------ .
Subtraction. Again, what we have been taught at grade school has been the unnatural way of getting results from right to left (from whose whim did we follow anyway?)
Here at Math is Easy; we try to revolutionize mathematical computation of starting from the left, then moving to the right. You have to admit, it is easier that way, as we have been largely conditioned for reading left to right. We don’t we compute left to right instead?
Here’s an example to work with using this method.
5, 4 7 8
- 2, 6 1 3
----------------------
? ? ? ?
Let’s start from 5 at the upper-left corner. Immediately move your eyes on the number to the right of 5, and notice that 4 is not enough to subtract 6 with. What you do is subtract at once 1 from 5, and carry over the 1 — in your memory — to 4, making it 14. Then subtract 2 from 4 in the thousands place.
4 5, 14 7 8
- 2, 6 1 3
-----------------------
2, ? ? ?
When you move to the hundreds place, immediately look at the tens place if it needs any help. We see that 7 is sufficient to subtract 1 with. So we proceed to subtracting 6 from 14.
4 5, 14 7 8
- 2, 6 1 3
------------------------
2, 8 ? ?
Do the same with the digits aligned at the tens and ones place.
4 5, 14 7 8
- 2, 6 1 3
------------------------
2, 8 6 5
Have you seen a pattern of thinking here? Aside from computing from left to right, we immediately looked at the numbers to the right, and see if they needed any carrying-over to do. This method of mental math should be superior to the traditional method, since it involves mental processes going from left to right.
This math skill is also sufficiently able to let you solve the problems quickly if there are multiple digits that need carry-overs. For example:
9, 0 2 6
- 4, 0 8 1
--------------------
? ? ? ?
As usual, we start at 9. Look for the zero in the hundreds place, but it seems we don’t need to subtract anything. Instead we look further down the stretch. The number 2 needs some help doesn’t it? Why don’t we borrow from 9?
8 9, 0 2 6
- 4, 0 8 1
---------------------
? ? ? ?
At once, subtract 4 to 8 before moving on, and mentally assign 1 to 0, making it 10.
8 9, 1 0 2 6
- 4, 0 8 1
-----------------------
4, ? ? ?
There isn’t anything to subtract from 10, so subtract 10 with 1 and carry it over to 2, making it 12.
89, 91 0 1 2 6
- 4, 0 8 1
-----------------------
4, 9 ? ?
Now, proceed subtracting as normal, down to the ones place.
89, 91 0 1 2 6
- 4, 0 8 1
-----------------------
4, 9 4 5
You could ask, well, this isn’t much different from the normal method of subtraction, and we would agree with you. But you’ve got to admit, it’s much more comfortable and natural, right?
To improve your math skills, here are some examples which you can work with:
110,826 69,411 3,745
- 109,771 - 43,008 - 1,709
--------- -------- -------
782,003 80,232 6,548
- 408,915 - 62,404 - 5,990
--------- -------- -------
Click here to go to your next lesson: Multiplication Strategies!
