Fluency and Strategies for Subtraction of Numbers
Subtraction is a mathematical operation where a number having a smaller value is removed from another number with a greater value. In the figure given below, there are a total of nine toy helicopters. After deducting four of the red toy helicopters, we are left with five of the toy helicopters of the other color.
Example: 9 – 4 = 5
We are already aware of the number line and the type of calculations that can be done using the same. When adding two numbers, we shift the given number of units to the right. For example, when adding two and one, the following is observed on a number line.
We get the answer as three when we shift one unit to the right after adding one. When subtracting two numbers, there is a slight change in the movement. If we were to subtract one from two, we first move two units to the right side of the number line, and then we move one unit to the left.
There is a connection between addition and subtraction.
Take a look at this sum.
20 + 10 = 30
Now, observe this.
If we subtract 10 from the sum total of 30, we get 20.
30 – 10 = 20
So, if the sum total of two numbers is provided, subtracting one number from the sum total gives us the other number. For instance, check the examples below.
45 + 35= 80
80 – 35 = 45
97 + 3 = 100
100 – 97 = 3
Now, we will discuss how we can decompose a number using subtraction. Let’s consider the subtraction of two numbers, ‘15’ and ‘8’. Using decomposition, the results will look like the following:
We have to find 30 – 18.
Eighteen can be split into 10 and 8.
Next, we subtract the number that was split from thirty.
30 – 10 – 8
So, first, we subtract ten from thirty
30 – 10 = 20
This gives us ‘20’. Next, we subtract eight from twenty.
20 – 8 = 12
This gives us the result as ‘12’.
Hence, 30 – 18 = 12. This is how a number is decomposed to give the result.
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Solved Examples
Example: Represent the results of the following subtractions on the number line and also by using the decomposition method.
- 20 – 14
- 18 – 13
Solution:
Part 1: Using the decomposition method, we split the numbers into multiples of ten and single digits.
20 – 14
20 – 10 – 4 (splitting 14 into 10 and 4)
20 – 10 = 10
10 – 4 = 6
In the number line, initially, we move up by twenty units. After this, ten units are removed. This means the dot moves to the left by ten units.
20 – 10 = 10
Afterward, the position moves down by four units.
So, 20 – 14 = 6.
Part 2: 18 – 13
18 – 10 – 3 (splitting 13 into 10 and 3)
18 – 10 = 8
First, we deduct ten from eighteen. This gives us ‘8’.
This is the number line for 18 – 10 = 8.
Now, we deduct three from eight, and we get the following result.
8 – 3 = 5
Hence, 18 – 13 = 5
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A number line gives a visual understanding of operations like addition and subtraction. Usually, when addition and subtraction are done, there is nothing that shows how these numbers are added or subtracted. This is where the number line helps a person understand what happens when these mathematical operations are conducted.
Decomposition is a method where a number is split into multiples of ten and a digit. This ensures that plotting the points is much easier. Usually, the multiple of ten is initially removed, followed by the digits. It is much easier to start with multiples of ten because the point under consideration lands on another number with the same units place. Next, a few digits are subtracted to get the final answer. Therefore, using the decomposition method is not necessary, but it makes the process much easier.