Subtraction of Multi-digit Numbers
Subtraction is one of the four arithmetic operations, the other three being addition, multiplication, and division. Subtraction is an operation where one or more objects are removed from a group. It is denoted by the minus sign ‘-’.
Let us understand this with an example. If Mack is holding 5 balloons and suddenly 2 of them burst, then only 3 balloons will be left with him.
This means that Mack now has 2 balloons less. This can be mathematically written as: the number 2 is subtracted from the number 5. In terms of subtraction, we can write it as,
5 Balloons – 2 balloons = 3 balloons
or
5 – 3 = 2
It is easy to subtract simple or single-digit numbers. However, the subtraction of multi-digit numbers is not that simple. For subtracting multi-digit numbers, the following methods can be used:
- Number line using count on and count back strategies.
- Mental math.
Let us explore each of these methods in detail.
Subtraction using a number line
We can subtract numbers on the number line. There are two ways to subtract a number on the number line: count back strategy and count on strategy.
Count back strategy
In this method, first mark the number on the number line from which you want to subtract. Then count back the number that is being subtracted from the marked point to the left. The new point obtained is the difference between the two numbers.
The count back strategy becomes easier if you first count back by ‘tens’ and then by ‘ones’.
For example, we can find 258 – 83 as,
Here, first draw a number line. Then mark ‘258’ on it.
To subtract ‘83’, first reverse count by ‘tens’, that is, 50 and 30. At last, count back by three ‘ones’ to reach the number ‘175’.
Therefore, the answer to the subtraction is:
258 – 83 = 175
Count on strategy
To find the subtraction result using the count on strategy, first draw a number line. Then mark the smaller number or the subtrahend that you want to subtract on the number line. Then start counting towards the right until you reach the number from which you want to subtract, that is, the minuend. The total sum of the skip counts gives the result of the subtraction.
For the same example, 258 – 83 :
First mark ‘83’ on the number line. Then skip count by ‘hundreds’ then ‘tens’ and then ‘ones’ to reach 258. At last, add the skip counts to find the difference.
Here we practice skip counting first by ‘hundreds’, that is 100, then by ‘tens’, that is 20 and 30, and at last by ‘ones’, that is 5.
Let us add the skip counts to get the difference,
100 + 30 + 50 + 5 = 175
Therefore, 258 – 83 = 175
Subtraction using mental math
Subtraction using mental math is the way by which we can subtract easily through compensation.
If any number in a subtraction equation is very near to a ‘tens’, ‘hundreds’, or thousands, just round off the number by changing it by a small amount. Then perform the subtraction operation to get an approximate result. Later, compensate for the small change by the reverse operation on the result to find the exact answer.
We can use compensation to change one or both the numbers in a subtraction equation. In case we change both numbers by the same amount, then no compensation is needed in the final result.
For example, If we want to find the result of 332 – 197 ,
We can see 197 is very close to 200, that is, we add 3 to the number 197. We add the same amount to the second number, 332, which will give us 335. Now the subtraction equation becomes, 335 – 200, which is relatively easier to calculate.
So, 332 – 197 = 135
Here we added 3 to both the numbers. Therefore, there is no need for compensation in the result.
135 is the exact difference.
Again, if we add 3 only to the number ‘197’,
Here, we subtracted 3 more to 197. So, we must add 3 to the answer to find the exact result.
132 + 3 = 135
Therefore, 332 – 197 = 135.
Subtraction of three-digit numbers
Subtraction of three-digit numbers can be estimated using rounding of numbers. Estimation can also be used to determine whether the answer is reasonable or not.
Here are the steps to estimate the difference between 2 three-digit numbers:
Step 1: Round the numbers to the nearest ‘hundreds’.
Step 2: Find the difference between the rounded numbers. This gives the estimated difference.
The exact difference can be calculated using the regrouping method. In the regrouping method, we start subtraction from the ‘ones’, then the ‘tens’, and finally the ‘hundreds’. If there are not enough ‘ones’ or ‘tens’ to subtract, regroup the numbers and repeat the same.
Regrouping implies that if for a particular place value, the minuend digit is less than the subtrahend digit, regroup by changing 1 ‘tens’ to 10 ‘ones’, or 1 ‘hundreds’ to 10 ‘tens’, and so on. Then do the subtraction.
(1 hundred, when moved to 10s place, becomes 10 ‘tens’. 1 ten, when moved to ‘ones’ place, becomes 10 ‘ones’.)
For example, in 3 ‘tens’ and 12 ‘ones’, 12 ‘tens’ can be written as 1 ‘tens’ and 2 ‘ones’, so a total of 3 + 1 = 4 ‘tens’, which makes it 4 ‘tens’ and 2 ‘ones’.
For example,
Let us estimate 504-216.
Round 504 to the nearest ‘hundreds’ as 500 and 216 to the nearest ‘hundreds’ as 200.
The difference is about 300.
Now let us find the exact difference.
We see that the digit 4 is not enough to subtract 6 at ‘ones’ place. So, we should regroup 1 ‘tens’ to 10 ‘ones’. However, at ‘tens’ place, the digit is 0, so we cannot regroup from ‘tens’ place. Therefore, move to ‘hundreds’ place and regroup 1 hundred to 10 ‘ones’, reducing the digit 5 to 4. At last, regroup 1 ‘tens’ from ‘tens’ place as 10 ‘ones’ at units place.
Finally, we get 4 ‘hundreds’, 9 ‘tens’, and 14 ‘ones’ in the minuend. Now perform subtraction as usual.
The exact result comes to 288. The estimated answer was 300, which is close to the exact answer and hence is reasonable.
Therefore, 504 – 216 = 288
Solved Multi Digit Subtraction Examples
Example 1: Use the count back strategy to find 275 – 35.
Solution:
First, mark 275 on the number line. Then count back 3 ‘tens’ or 30. Then count back 5 ‘ones’. The number obtained on counting back is 240.
Therefore, 275 – 35 = 240.
Example 2: Use the count on strategy to find 123 – 44
Solution:
First, mark 44 on the number line. Then skip count 50, 20, and 9 to reach the number 123.
Therefore, the summation of the skip counts is 50 + 20 + 9 = 79.
Therefore, 123 – 44 = 79.
Example 3: A store owner has 220 laptops. He sells 102 of them. Then he receives an order for 130 laptops. Does he have enough laptops to complete the order?
Solution:
The store owner sold 102 of the laptops. Subtract the sold laptops from the stock of the store owner to get the remaining number of laptops. Then compare the remaining number of laptops in stock with the required number of laptops.
Therefore, 220 – 102 = 118.
The storekeeper has 118 laptops left, but the order is for 130 laptops, which is higher than the number of laptops remaining in stock. Therefore, the storekeeper cannot complete the order.
Example 4: A movie theater has 227 seats. 104 seats have been booked. How many seats are available?
Solution:
We will subtract the booked number of seats from the total number of seats to get the available seats.
227 – 104 = ?
We can use mental math to calculate the number of seats available. 104 is close to 100. We subtract 4 from 104 and find the approximate solution.
Now, since we subtracted 4 less, we again subtract 4 from the answer to find the exact answer,
127 – 4 = 123
Therefore, 227 – 104 = 123 .
There are 123 seats available in the cinema hall
No, the answer remains the same as the minuend and subtrahend are the same.
Imagine you have 8 apples and your friend asks for 12 apples. Is it possible for you to give her 12? No, so 8 – 12 is not possible.
However, if we continue marking the number line in the negative direction and reverse skip count, we can get the difference as a negative number. You will learn more about negative numbers in higher grades .
If we add and subtract the same number from a given number, the result remains the number itself. For example,
If we have the number 10 and we add 5 to 10, we get 5 + 10 = 15. From this, we subtract 5, so 15 – 5 = 10. Here, we added and subtracted the same number, that is, 5, to the number 10 to get the number we started with, which is 10 itself.