Subtraction with Regrouping

Remember the following rules of subtraction:

Rule-1

The result in subtraction is called the difference.

Rule-2

When zero is subtracted from a number, we get the same number as result.

Rule-3

When a number is subtracted from itself, we get zero as result.

Rule-4

While subtracting, always place the bigger number above the smaller number.

Revise regrouping tens and ones:

4 tens 5 ones = 3 tens 15 ones

8 tens 3 ones = 7 tens 13 ones

6 tens 4 ones = 5 tens 14 ones

7 tens 1 ones = 6 tens 11 ones

2 tens 3 ones = 1 tens 13 ones

Out of 62 students in a class, 16 students did not go to the school picnic. So how many actually went for the picnic?

Step 1: To subtract 16 from 62 arrange numbers in proper columns. Write the bigger number on top and the smaller number under it.

Step2: subtract digit in ones column first. Since 6 ones is greater than 2 ones, we need to borrow 1 ten from the tens column. 2 ones will now become 12 ones.

12ones – 6 ones = 6 ones

Step 3: now we move to tens column. Since one tens has been borrowed from the tens column, it has become 5 tens. Therefore, 5 tens – 1 tens = 4 tens

Examples

Example: subtract 473 from 721

Step 1: Arrange under proper columns.

Step 2: subtract ones first. 1 one is smaller than 3 ones. So, we borrow 1 ten from tens column. 1 one now becomes 11 ones. So, 11 ones – 3 ones = 4 ones

Step 3: subtract tens. 1 tens – 7 tens

1 tens is smaller than 7 tens

So we borrow 1 teens from the hundreds column.

1 tens now becomes 11 tens

So, 11 tens – 7 tens = 4 tens

Step 4: subtracts the hundreds.

6 hundreds – 4 hundreds = 2 hundreds

The answer is 248.

some examples are:

Step1: Arrange the numbers in the column wise fashion.

Step2: Now subtract the ones digit of both the numbers, if the ones digit of the subtrahend is greater than the ones digit of the minuend then borrow from tens digit else do the subtraction, no need to take any borrow.

Step3: Now subtract the tens digit of both the numbers,if the tens digit of the subtrahend is greater than the tens digit of the minuend then take a borrow from then hundreds digit else do the subtraction, no need to take any borrow.

Step4: now subtract the hundreds digit of both the numbers, if the hundreds digit of the subtrahend is greater than the hundreds digit of the minuend then take a borrow from then thousands digit else do the subtraction, no need to take any borrow.

Step5: now subtract the thousands digit of both the number.

some examples are:

Example: subtract 2736879 from 5342568.

Solution: here minuend= 5342568 and subtrahend = 2736879

Arranging the digits of the given number in common form and subtracting column wise, we get:

Hence, 5342568 – 2736879 = 2605689

Explanation:

Subtracting ones place:

We cannot subtract 9 ones from 8 ones.

So, we borrow 1 ten, leaving behind 5 tens.

Now, 1 ten + 8 ones = 10 ones + 8 ones = 18 ones

And, 18 ones – 9 ones = 9 ones.

Write 9 under ones column.

Subtracting tens place:

We cannot subtract 7 tens from 5 ones.

So, we borrow 1 hundred, leaving behind 4 hundreds.

Now, 1 hundred + 5 tens = 10 tens + 5 tens = 10 tens + 5 tens = 15 tens

Write 8 under tens column

Subtracting hundreds place:

We cannot subtract 8 hundreds from 4 hundreds

So, we borrow 1 thousand, leaving behind 1 thousand

Now, 1 thousand + 4 hundreds = 10 hundreds + 4 hundreds

= 14 hundreds.

subtracting thousands place:

And, 11 thousand – 6 thousand = 5 thousands

Write 5 under thousands column.

Subtracting ten- thousands place:

3 ten- thousands – 3 ten thousands = 0 ten- thousands

Write 0 under ten-thousand column.

Subtracting lakhs place:

We cannot subtract 7 lakhs from 3 lakhs.

So, we borrow 1 ten-lakh, leaving behind 4 ten-lakhs

And, 13 lakhs – 7 lakhs.

Write 6 under lakhs column.

Subtracting ten-lakhs place:

4-ten lakhs – 2 ten-lakhs = 2 ten- lakhs

Write 2 under ten-lakhs column.

Hence, the difference between the given numbers= 2605689.

Example: find the difference between 2687934 and 6345148.

Solution: here both the given numbers are 8-digit numbers

Comparing their leftmost digits, we find that 2<6.

Therefore, 26879354 < 6345148

So, minuend = 63457148

Arranging the digits of the given numbers in column form and subtracting column wise, we get:

Hence, the difference between the given numbers = 36577794.

Introduction to Subtraction With Regrouping, What is Subtraction With Regrouping?, Working on Subtraction With Regrouping