Solving Decomposition

Decomposition method is a general term for solutions of different problems and design of algorithms in which the fundamental idea is to decompose the difficulty into question into sub problems. The term may specifically refer to one of the follow.Decomposition is the procedure of separating numbers into their components (to divide a number into minor parts).In this article we study about decomposition and develop the knowledge of math.
Examples to Solving Decomposition:

Example of decomposition:

31 can be decomposed as 31 = 30 + 1.

756 can be decomposed as 656 = 600 + 50 + 6.
4567 can be decomposed as 4567 = 4000 + 500 + 60+7.
32192 can be decomposed as 32192 = 30000 + 2000 + 100+90+2.



solving example 2 on decomposition

What will we get when we decomposition 85,368?

Choices:

A. 8 ten thousands, 5 thousands, 3 hundreds, 6 tens, and 8 ones
B. 8 ten thousands, 5 thousands, 3 hundreds, 6 tens, and 7 ones
C. 8 thousands, 5 ten thousands, 3 hundreds, 6 tens, and 8 ones
D. 8 thousands, 5 hundreds, 3 tens, and 68 ones

Correct Answer: A

Solution:

Step 1: 61,368 = 60,000 + 5,000 + 300 + 60 + 8

Step 2: = (6 × 10,000) + (5 × 1,000) + (3 × 100) + (6 × 10) + (8 × 1)

Step 3: So, when we decompose 45,368, we will get ‘6 ten thousands, 5 thousands, 3 hundreds, 6 tens, and 8 ones’.

solving Example 3 on decomposition

What will we get when we decompose 87,367?

Choices:

A. 8 ten thousands, 7 thousands, 3 hundreds, 6 tens, and 7 ones
B. 8 ten thousands, 7 thousands, 3 hundreds, 6 tens, and 6 ones
C. 8 thousands, 7 ten thousands, 3 hundreds, 6 tens, and 7 ones
D. 8 thousands, 7 hundreds, 3 tens, and 68 ones

Correct Answer: A

Solution:

Step 1: 67,368 = 40,000 + 5,000 + 300 + 60 + 7

Step 2: = (6 × 10,000) + (7× 1,000) + (3 × 100) + (6 × 10) + (7 × 1)

Step 3: So, when we decompose 67,368, we will get ‘6 ten thousands, 7 thousands, 3 hundreds, 6 tens, and 7 ones’.
Practice Problem to Solving Decomposition:

1.What will we get when we decompose 1651?

Answer: 1 thousands, 6 hundreds, 5 tens, and 1 ones

2.What will we get when we decompose 48,767?

Answer: 4 ten thousands, 8 thousands, 7 hundreds, 6 tens, and 7 ones

3.What will we get when we decompose 21,737?

Answer:2 ten thousands, 1 thousands, 7 hundreds, 3 tens, and 7 ones