Monday, 16 January 2012

Compose and Decompose Numbers in Grade III

Hello friends, today we are going to learn about Compose Numbers and Decompose Numbers for Grade III of central board of secondary education. We are discussing both Compose Numbers and Decompose Numbers one by one. So firstly compose numbers, compose numbers also called composite numbers. A positive integer which is not a prime number(what are prime numbers) is called composite or compose number that is n>1 which has factors other than 1 and itself also. Where n is a composite number. If it is not a Composite Number then it is called a Prime Number. In other words a number which can be divided evenly by numbers other than 1 or itself is called a compose number. The example of composite numbers is 4, 6, 8, 9, 10, 12, 14, and 15. what is prime factorization of these numbers its shown in the following table.
             n                             Prime factorization                       n                     prime factorization
            4                                     22                                       20                            22.5
            6                                     2.3                                     21                            3.7
            8                                     23                                      22                             2.11
             9                                    32                                       24                             23.3
           10                                   2.5                                      25                             52  
           12                                   22.3                                     26                             2.13
           14                                   2.7                                      27                             33
           15                                  3.5                                      28                              22.7
Now I am taking an example that may help you to understand composite numbers. We take two numbers that is 4 and 7. 4 can be divided evenly by 2 but 7 is not.
4 can be divided evenly by 2, as well as by 1 or 4,
4=1 x 4
4=2x2
But in the case of 7, we cannot divide 7 evenly by 2,3,4,5.
4 can be divided evenly so it is a Composite Number and 7 cannot be divided evenly so it is a Prime Number. 7 can only be divided evenly by 1 or itself. So from the above composite means something made by combining things like numbers.To know about highly composite numbers click here.
Now I am going to tell you about Decompose Numbers. Decompose Numbers is just reverse of composite numbers. In composite we combine things and made something but in decompose we separate or break down those things. Decompose is defined as the process of separating numbers into their components or to divide in to smaller parts is called Decompose. When we decompose a number then it is written as a product of prime factors and when  we decompose a fraction then it is written as a sum of partial fractions. For example      
356 can be decomposed as 356 = 300 + 50 + 6. I am taking one more example which may help you to understand the decompose numbers. We decompose 25,541.
Firstly, 25,541 = 20,000 + 5,000 + 500 + 40 + 1
= (2 × 10,000) + (5 × 1,000) + (5 × 100) + (4 × 10) + (1 × 1)
From the above, when we decompose 25,541 then we will get ‘2 ten thousands, 5 thousands, 5 hundreds, 4 tens, and 1 ones.
I want to tell you one more thing, when we multiply a list of prime numbers together, are equal to that number is called  prime decomposition of a number. For example 24=2x2x2x3, its prime decomposition is 2, 2, 2, 3.
From the above discussion I hope that it would be helpful you to understand the Compose Numbers and Decompose Numbers and to know about Numbers in Grade IV and Multiplication facts/tables you can refer to the various sites available on internet.

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