Decomposing and Composing Numbers

Introduction :

Decomposing and composing numbers is the very old concept in number system and mathematics. It means to take numbers apart into their tens and ones form. The smaller problem should be simpler than larger problem, so by using decomposing, large problems into simple problems. Larger problems can be tackled with ‘divide and conquer”. So we are using decomposing and composing numbers.


Discussion on Decomposing and Composing Numbers

Decomposition:

Decompose the problem so that:

Each sub problem is at the same level of detail,
Each sub problem can be solved independently,
The solutions to the sub problems can be combined to solve the original problem.
Composition:

Each sub problem is at the different level,
Each sub problem can be solved dependently not to be easy one,
The solutions to the sub problems cannot be combining to solve the actual problem.


Advantages of decomposing and composing numbers:

Different people can workout on different sub problems,
Parallelization may be possible,
Maintenance is easier.


Disadvantages of Decomposition and composition:

The solutions to the sub problems might not combine to solve the original problem,
Poorly understood the problems are hard to decompose.

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Some Example Problems on Decomposing and Composing Numbers

To begin the decomposing numbers you must take a 2- digit number apart, like this.

45 = 40+5

So, 45 is the same as saying 40+5, because the 4 in 45 stands for 40,

And the 5 in 45.

45 stand for 5,

Example 1: 53 + 25 =?

First add the tens ….. 50 + 20 = 70

Add the ones …            3 + 5   = 8

Then add the sums! And get the answer as,

70 + 8 = 78

Example 2: 154 + 32 =?

First add the hundreds, and then add tens and finally add ones….

100 + 50 + 30 + 4 + 2 totally add all, the sum is,

100 + 50 + 30 + 4+ 2 = 186, so get the answer is 186.

Example3: Choose the correct expression that will result in 818.

a)      200 + 200 + 200 + 10 +8

b)      250 + 250 + 200 +10 + 8

c)      200 + 200 + 200 + 200 + 10 + 8

d)      200 + 200 + 200 + 18

Solution:

Answer is c) 200 + 200 + 200 + 200 + 10 + 8

Steps to derive:

Simplify given answer chose one by one

200+200+200+10+18 = 618, and

250+250+200+10+8 = 718, and

200+200+200+200+10+8 = 818, and

200+200+200+18 = 618.

Hence the right option (choice) is “c”

So the answer is 200+200+200+200+10+8 represents = 818.