Strategies for Addition and Subtraction of Multi-digit Numbers
There are many ways or strategies that are applied to the addition and subtraction of multi-digit numbers. Some are used for smaller or simpler numbers, while others are used for greater or complex numbers.
It is the foundational skill that students in lower grades must develop in order to tackle many tricky questions on addition and subtraction in the later grades.
These strategies that we’ll soon look at give students different ways to approach problems involving addition and subtraction.
Strategies for the Addition Operation for Multi-digit numbers
The addition operation for multi-digit numbers is a very basic operation that children need to learn in the lower grades.
In an addition operation, the numbers being added are called addends, and the result is called the sum.
There are many strategies for adding multi-digit numbers, such as:
- Use of partial sum
The partial sum method is a 2-step process and uses the concept of place value in numbers.
In this method, corresponding digits in the place value column are added, starting from the left to the right, to generate the partial sums.
These partial sums are then added together to get the required sum.
For example, 123 + 242,
123 can be broken down as 100 + 20 + 3
Similarly, the number 242 can be broken as 200 + 40 + 2
Now add the digits of both numbers at the hundreds place, that is, 1 + 2 = 3, hence, 3 hundreds. Similarly, add the digits of both the numbers at the tens place and the ones place respectively, that is, 2 + 4 = 6, which makes 6 tens and 3 + 2 = 5, or 5 ones.
As mentioned above, the partial sum method is a two-step process.
In the first step, the digits in the place value column are added to get the partial sum of two numbers.
In the above figure, 300, 60, and 5 are partial sums obtained after adding the digits in the respective place value columns.
In the second step, these partial sums are added to get the final sum, 365.
- Use of Compensation:
As the name suggests, in this method, the addends are increased or decreased by a very small number to make the number simpler and the addition process easy.
Later, this addition or subtraction of a very small number is compensated in the sum to get the final sum.
For example: 520 + 229
Upon adding 1 to 229, it becomes 230, which makes the addition of the given numbers easy.
520 + 229
⇒ 520 + 230
⇒ 750 → 750 – 1 = 749 [To compensate for the 1 added initially].
- Use of counting on:
It is a basic mental strategy to add numbers. Usually, we take the larger number and count up from there.
For example: 45 + 6
First, we take the larger number of the two, which is 45 here.
Then count up 6 times from there, that is, 46, 47,…51, we get 51.
Hence, the sum is 51.
- Using regrouping:
It is a method of addition in which ten ones are regrouped into one tens, or ten tens are grouped into one hundreds, or ten hundreds are grouped into one thousands and so on.
It is generally used when the sum of the digits in a place column exceeds 9.
For example: 145 + 236
In the above example, the sum of digits at the ones place is greater than 9, that is, 5 + 6 = 11, hence a +1 is carried over is shifted to the tens place digit, 4. It is added to the digit 4 to make it 5. Then the usual addition process is applied.
Strategies for the Subtraction Operation for multi-digit numbers
Subtraction is one of the four basic operations of arithmetic in which the difference between two numbers is calculated. In a subtraction equation, the larger number from which the smaller number is subtracted is known as the minuend, and the smaller number being subtracted is known as the subtrahend.
The result of subtraction is called the difference.
Similar to addition, several strategies can be used to subtract numbers.
- Use of partial difference:
It is a two-step process similar to the partial sum method used in addition. The only difference between them is that here partial differences are obtained by subtracting respective digits from the place value column of the two numbers. And these partial differences are then added to get the result of the subtraction.
- Use of compensation:
Subtraction by compensation is a strategy similar to addition by compensation.
In this method, the minuend or subtrahend is either increased or decreased by a very small number, which is later compensated in the final result.
For example: 249 – 120
If 1 is added to make the number 249 → 250, the subtraction will be easier.
249 – 120
⇒ 250 – 120 (1 is added to 249)
= 130 → 130 – 1 = 129 [-1 is used to compensate]
Consider another example, 321 – 50
If 1 is subtracted to make the number 321 → 320, the subtraction will be easier.
321 – 50
320 – 50 (1 is subtracted from 321)
= 270 → 270 + 1 = 271 [+1 is used to compensate]
- Use of counting on:
It is a very basic method of subtraction in which we count downward from the number from which another number is being subtracted.
Also, the other number being subtracted should be a smaller number.
For example, 42 – 5
In this, we count 5 times downward from 42.
41,40….,37, hence we get 37 as the difference.
- Use of regrouping:
It is the opposite of the regrouping method used in addition.
In this method, one ten is converted into ten ones, or one hundredth is converted into ten tens and so on.
For example: 245 – 126
Since the digit at ones place of the subtrahend is 5, which is less than the ones digit 6 of the minuend, we will borrow 1 tens from the digit at the tens place, that is, 4, making it 15 and the digit 4 becomes 3 as it has lost one tens to the one place.
5 → 5 + 10 = 15
4 – 1 → 3
Now the subtraction can be done as usual.
Solved Addition & Subtraction of Multi Digit Number Examples
Example 1: If Noah has 134 candies and Daisy has 247 candies, how many candies do they have in total?
Solution:
Noah → 134 candies
Daisy → 247 candies
Using the regrouping method,
The total number of candies both Noah and Daisy have is,
= 134 + 247
= 381 [Add]
Hence, Noah and Daisy have 381 candies in total.
Example 2:
Newton buys a pack of toothpaste worth $2. If he gives the cashier a bill of $5, how much money will Newton get back from the cashier?
Solution:
Newton has $5 cash.
He spends $2 on the toothpaste.
Using the counting on method, we count down from 5 twice,
$5, $4, &3
= $3
Hence, the cashier will return $3 to Newton.
Example 3:
Robert buys a house worth $240,000. He spends $20,000 on the furniture for the house. How much does he spend in total?
Solution:
Using the partial sum method,
$240,000 + $20,000 (Add)
= $260,000
Hence, Robert spends a total of $260,000.
Example 4:
Elijah buys a pack of glitter pens for $21. If he gives the cashier a bill of $9, how much more will he have to pay him?
Solution:
Using the compensating strategy,
$21 – $9
If 1 is added to make the number 9 → 10, the subtraction will be easier.
$21 – $10 [subtract]
= $11 → $11 + $1 = $12 [To compensate -$1]
Hence, Elijah has to pay $12 more to the cashier.
Below are a few strategies used in addition.
- Addition by regrouping
- Addition by compensation
- Addition by the partial sum
- Addition by count on
Below are some of the strategies used for subtraction.
- Subtraction by compensation
- Subtraction by regrouping
- Subtraction by the partial sum
- Subtraction by counting on
Addition and subtraction are very important for certain activities in everyday life such as, making changes in the quantity of groceries in a supermarket, playing certain games that involve subtraction or addition of the points scored, keeping a record of finances, and so on.