Subtraction of Numbers using the Decomposition Method (Definition, Types and Examples) - BYJUS

# Subtraction of Numbers using the Decomposition Method

Decomposing numbers helps us reimagine a number in multiple ways. For example, 24 can be written as 20+4 or 30-6. We can use this to our advantage while performing basic calculations like addition and subtraction. Using this concept, we can easily subtract multi-digit numbers by borrowing from digits of a number having a higher place value. ...Read MoreRead Less

## What are minuend and subtrahend?

A subtrahend is the number that we subtract from another number in a subtraction sentence. In a subtraction sentence, the minuend is the first number. To find the difference, subtract the subtrahend from the minuend. The minuend is the number at the top of the vertical or column method of subtraction.

## What is the decomposition method?

“Decomposing a number” is a term used in mathematics to describe the process of breaking a number apart. Try to come up with all the different ways to make 9 to see decomposition in action. 4 + 5, 2 + 7, 0 + 9, or 1 + 8 could have been the two parts you came up with to make 9. These various parts are decomposed numbers starting at 9.

A ten is borrowed (traded) from the top number in the next column on the left, and that number is marked down by one in its place value, in the column method of subtraction.

The example given below shows the decomposition method:

## Why do we decompose the subtrahend?

In subtraction, the decomposing or “break apart” strategy is slightly different. Only the subtrahend (smaller number) should be decomposed, and then each place value should be subtracted from the minuend. When it comes to adding and subtracting, students can choose one strategy that works best for them.

Example: Suppose we have an expression such as 42 – 38.

If you’re employing a partial differences technique, break down the number into its place values (for example, 42 may be decomposed into 40 + 2).

However, this isn’t always helpful because you’ll wind up subtracting negative numbers, which can cause even more difficulty, particularly for younger students.

It will be 40 + 2 – 38. As we can see,  it is not the correct way to subtract 38 from 2, so here we have to decompose the subtrahend. Therefore, 38 can be subtracted from 42 in a way that firstly 8 is subtracted from 12.

Then, at tens place we have 30, and when we subtract 30 from 30 we get zero.

## Explain the concept of decomposition for 1 digit and 2 digit subtrahends

42 – 33

We can’t subtract or subtract 3 from 2 in the ones place column because 3 is greater than 2. If you  have only 2 apples, your sister won’t be able to take 7 apples from you. As a result, we must employ the decomposition procedure. When we borrow an amount from the number on the left and give it to the number on the right, decomposition occurs or is required. This is only for the numbers in the top row.

This means, we can’t get 3 from 2, so we borrow a ten from the column after that (the 4). We’ll deduct 10 from the left-hand number (4) and apply it to the right-hand number (2). Because the 4 is in the tens column, it equals 40 (4 10). Taking 10 from 40 results in 30 (2), and adding 10 to 2 results in 12.

42

-33

____

As 2 is smaller than 3, we have to take one from the tens column and perform the subtraction on one column.

We can now subtract 3 from 12 in the ones column to get 9.

42

-33

____

9

As 1 is transferred to one column. 3 is left in the tens column. Next, we subtract 3 from 3 in the tens column to get 0.

42

-33

____

09

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## Examples

Example 1: Solve the given expressions

(a) 23 – 14

(b) 31 – 12

Solution:

Part (a)

23

-14

____

As 3 is smaller than 4, we have to take one from the tens column and perform the subtraction on one’s column.

We can now subtract 4 from 13 in the ones column to get 9.

23

-14

____

9

As 1 is transferred to one’s column. So, 1 is left on the tens column. Next, we subtract 1 from 1 in the tens column to get 0.

23

-14

____

09

Part (b)

31

-12

____

As 1 is smaller than 2, we have to take one from the tens column and perform the subtraction on one’s column.

We can now subtract 2 from 11 in the ones column to get 9.

31

-12

____

9

As 1 is transferred to one’s column.  2 is left on the tens column. Next, we subtract 2 from 1 in the tens column to get 1.

Example 2: Solve the given pictorial problem using the decomposition method.

Solution:

We have the last number as 47, and 8 is subtracted from it.

As 7 is smaller than 8, we have to take one from the tens column and perform the subtraction on one’s column.

We can now subtract 8 from 17 in the ones column to get 9.

47

– 8

____

39

Now, the middle number is 33, and we have 39 in the next box, as shown in the image.

39

-33

____

06

We have to subtract 06 from 39, then the result will be 33, as shown above.

Now, 5 is subtracted from 33. As 3 is smaller than 5, we have to take one from the tens column and perform the subtraction on one’s column.

We can now subtract 5 from 13 in the ones column to get 8.

33

– 5

____

28

Example 3: Tom had $150 for the movie., and He spent$123 on the movie and snacks. Find the amount of money left after the movie.?

Solution:

The total amount of money Tom has is $150. He spent$123 on movies and snacks.

150

-123

_____

27

The pictorial image below  shows the decomposition method for the given problem:

Hence, Tom will save \$27 after watching the movie.

## Math Curriculum for all Grades

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Decomposing a problem into basic operations, such as addition, subtraction, multiplication, and division, indicates that we are breaking numbers down into smaller parts to make them easier to understand and solve.

The term “prime factorization” refers to the process of expressing a composite number as the sum of its prime factors. We divide 25 by its smallest prime factor, which is 5. So, the prime factorization of 25 is: 5 × 5 = 25 or 25 ÷ 5 = 5

We can use the concept of decomposing and composing numbers to help students improve their number sense and understanding of place value. Some people see 87 and realise it’s very close to 100, so they might want to break up the 87 to make it more appealing.

concepts. By looking at what your child is doing correctly and which concepts they understand, you can determine ways to practice areas that they are still developing.