Sunday, 27 July 2008

Mental Addition - a faster way to solve and impress

Maths can be fun when done in a unique way.
This post is about the way mental addition is done and its benefit.

In school, we are always taught to add numbers starting from the right-sided digit, then move on to the left-sided digit. This is the conventional way of doing addition.

But this has a demerit in that the first mention of a number to the answer starts from the right. We normally says a number starting from the LEFT!

On paper, this right to left method of addition is fine, but to do it mentally, it is a bit tricky.

For mental addition, we need to start addition from the left digit (as opposed to the conventional right side).

Let's start with an example.

4 5
1 2 +

We do the 4 + 1 = 5 first.
(Left side first)
Later do 5 + 2 = 7

Answer is 57.
(This is correct based on the traditional right to left addition also)

We can mentally compute this and say out the number directly as we have started with the left digit addition first which coincide with the left side saying.

Try another examle:

1 3 4
4 2 3+
The answer is 557 ! Easy?

Before we can finalised the number to a particular digit, look at the next digit and check if the addition of that 2 numbers in that digit position will be more than 10.

If the added sum of the next digit is more than 10, we need to add 1 to the current digit.

See next example.

Example (next level up):
2 3 6
1 2 5 +

The left digit final sum will be 2 + 1 = 3, and will not change since the addition of the next digit numbers will not be more than 10, therefore no carry over of 1.

Next, we do the addition to the centre digits which gives us 3 + 2 = 5, BUT look at the right digit summation.

It is 6 + 5 = 11 which is more than 10.

This will affect the centre digit final number by adding 1 to the initial 5.
Centre number answer ==> 5 + 1= 6.

Lastly the right digit number will be 1 (taking only the last number in the 6+ 5 = 11 answer).

Answer therefore = 3 6 1.

Mental maths has the advantage that the answer format matches the presentation format, which save time in flipping the final answer as done using the traditional or conventional method of right to left sequence of addition.


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