Subtraction is a basic mathematical operation, and it is used to compare the difference in numerical values of different numbers. To subtract two numbers, we can use various methods or strategies and one such method is subtraction by regrouping.
In subtraction by regrouping, we group the ones, tens, hundreds, and so on. We then use the regrouped numbers to find the difference.
Let us try to understand with an example.
We have 23 apples in a box. If we take out 17 apples, then how many apples are left in the box?
Let us see this in the form of a diagram:
This can also be shown using a subtraction equation as follows:
Now if we mix up these two, that is the diagram and the equation together we can see that the subtraction is as follows:
So clearly we cannot take away 7 apples from 3. This is where regrouping helps us. We will regroup the apples in the tens place and borrow one tens from it.
Now, as we see that there are 13 ones in the ones place, so we can subtract 7 from 13. Also, the tens place of 23 now has 10 apples, as we borrowed 10 apples for the ones place. The tens place in 17 also has 10 apples. So the final subtraction can be seen as follows:
So clearly we can see that 6 apples are left in the basket.
Now, this can also be done numerically. Let us find out more about it:
Upon arranging the digits of both numbers according to their place values and then subtracting them, we get;
So we borrow a ten from the tens place.
Since 1 ten is equal to 10 ones, 3+10=13 ones
So we will subtract 7 from 13 and take out one from the tens place.
Now, let us subtract the digits at the tens place,
So clearly using both the methods we get the answer as 6 apples. We will use this numerical subtraction method more often as it is easy to perform.
Let us see some solved examples of subtraction using the regrouping method.
Find 84 – 56.
For the subtraction, we grouped the digits in the ones place of the first number with the digit in the ones place of the other number.
Since 6 is greater than 4, it cannot be subtracted from 4. Therefore, we will borrow 1 ten from the tens place, and then convert it into 10 ones.
The digit in the ones place becomes 4 + 10 = 14 ones.
The operation proceeds as follows:
14 – 6 = 8 – In the ones place
7 – 5 = 2 – In the tens place
This can also be seen using a cube model as shown below:
Hence the difference is 28.
Find 13 – 7
Hence the difference is 6.
Is there a greater difference in the number of people attending college on Friday and Saturday, or Thursday and Friday?
For Friday and Saturday the difference is
52 – 44 = 8
For Thursday and Friday, the difference is
61 – 52 = 9
On comparing the two differences we find out that the number of students attending college on Thursday and Friday is greater than the number of students attending college on Friday and Saturday.
There were 60 cherries initially on a cherry tree. Elijah then plucked some cherries from it, and now there are 42 cherries left on the tree. How many cherries did Elijah pluck from the tree?
Initial number of cherries on the vine = 60
Cherries left on the vine after Elijah took some from it = 42
Then according to problem cherries taken by Elijah are:
60 – 42
So Elijah plucked 18 cherries from the vine.
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The following are a few words that indicates that we need to apply subtraction: