Subtraction must involve regrouping (borrowing) when the bottom digit in any column is larger than the digit above it. In one sense, borrowing is the reverse of the carrying what we have in addition.

1. Regrouping is not required when the minuend in 1's, 10's , 100's or 1000's places is greater than the subtrahend.
2. If zero (0) is subtracted from a number, the difference we get is the number itself, 6-0 =6
In this section we will be leaning more about subtraction with regrouping.

## Step by Step Subtraction with Regrouping

For the subtraction with regrouping, first arrange the numbers according to their place values and follow the rules as given below

1. Arrange the numbers: Arrange the number according to their place value.
8 6 4
5 9 5

2. Subtract the ones:

5 14

8 6 4
5 9 5
9

Here $5$ is bigger than $4$. So borrow $1$ ten.

$1$ Ten + $3$ once = $13$ once

$13 - 5 = 8$

3. Subtract the tens:

7 15 14

8 6 4
5 9 5
6 9

Here $9$ is bigger than $5$. Borrow $1$ hundred.

$1$ hundred + $5$ tens = $15$ tens

$15 - 9 = 6$

4. Subtract the hundreds:

7 15 14

8 6 4
5 9 5
2 6 9
Here $7$ is left on hundred's place. Subtract $5$ from $7$

$7 - 5 = 2$

## Subtraction with Regrouping Practice

The following are the practice problems for subtraction with regrouping.

### Solved Examples

Question 1: Solve $82 - 35$
Solution:

We can arrange the number according to their place values

82 = 8 tens + 2 ones
35 = 3 tens +  5 ones

we can not subtract immediately, because 5 is larger than 2. we borrow 1 ten from the 8 tens in the tens column.

Hence we can rewrite the number 82 as

8 tens + 2 ones = 7 tens  + 1 tens + 2 ones

= 7 tens + 12 ones

Now, its possible to subtract,

82 = 8 tens + 2 ones =  7 tens + 12 ones
-35 = 3 tens    5 ones =   3 tens    5 ones
4 tens + 7 ones

The result is $82 -35 = 47$

Question 2: A farmer collected 563 apples from his orchard. He sold 365 apples in the market. How many apples are left with him?
Solution:

Apples in the orchard    = 5  6  3
Apples sold                     = 3  6  5
Apples left                        = 1  9  8