There, we covered the use of Subtraction Table and a number of examples on Subtracting two digit numbers.

That knowledge is a prerequisite here.

Here, we deal with three digit numbers.

Subtraction of three digit numbers

We have already seen in decimal number system that the successor to 99 is 100. or the predecessor to 100 is 99.

i.e. 100 - 1 = 99.

Let us present this process in the vertical presentation by using the borrow method (also called regrouping method) explained in Subtraction of Two Digit Numbers.

1^{0}0^{9}0^{10}
1
----
99
----

First we have to subtract bottom digit in the units' place from the upper digit in the units' place.

i.e. we have to subtract 1 from 0. But 1 is bigger than 0.

So, we have to borrow one (one10) from the digit in tens' place i.e. 0.

0 as it is can not give 1. So it borrows 1 (one10) from the 1 in hundreds' place.

Because of this borrowing, 0 in units' place becomes 10 and 0 in tens' place with the borrowed 10 becomes 9 and 1 in hundreds' place becomes 0.

Now subtract 1 from 10 which gives 9 in the units' place.

In Tens' place, we have to descend the 9 since there is nothing to subtract in tens' place.

What is left in hundreds' place is only 0 which can be ignored.

So the answer is 99.

See 0 in the units' place is sriked off to become 10,

and 0 in the tens' place is sriked off to become 9,

and 1 in the hundreds' place is sriked off to become 0.

Thus 100 - 1 = 99. Ans.

We also saw in the decimal number system, that the three digit numbers range from 100 to 999.

Knowing these numbers in figures and in words is a prerequisite here.

In 3 Digit Subtraction, this borrowing will go one place further.

Solution to Example 1 of 3 Digit Subtraction : The vertical presentation of the problem is shown below.

725
189
-----
-----

First we have to subtract bottom digit in the units' place from the upper digit in the units' place.

i.e. we have to subtract 9 from 5.

But 9 is bigger than 5. So, we have to borrow one (one10) from the digit in tens' place i.e. 2.

Because of this borrowing, 5 in units' place becomes 15 and 2 in tens' place becomes 1.

Now subtract 9 from 15 which gives 6 in the units' place.

Now, we have to subtract bottom digit in the tens' place from the upper digit in the tens' place.

i.e. we have to subtract 8 from 1.

But 8 is bigger than 1. So, we have to borrow one (one10) from the digit in hundreds' place i.e. 7.

Again recall that,

When we borrow 1 from the immediate left digit, that borrowing makes the digit in the right place increase by 10. This is so, because the immediate left place value is 10 times the place value of the right.

Here the borrowing is applied from hundreds' place to the tens' place.

Because of this borrowing, 1 in tens' place becomes 11 and 7 in hundreds' place becomes 6. Now subtract 8 from 11 which gives 3 in the tens' place.

Now subtract 1 from 6 which gives 5 in the hundreds' place.

So the answer is 536.

This process is shown in the vertical presentation below.

7^{6}2^{11}5^{15}
189
----
536
----

See 5 in the units' place is sriked off to become 15,

and 2 in the tens' place is sriked off to become 11.

2 in the tens' place first became 1 by giving 1 to units' place and later became 11 by borrowing 1(one 10) from hundreds' place.

These two steps are not shown seperately.

7 in the hundreds' place is sriked off to become 6.

Thus 725 - 189 = 536. Ans.

Check : You may add 536 and 189 and check whether it is equal to 725 or not.

536
189
_{1}_{1}
---
725
---

It is verified to be correct.

Example 2 of 3 Digit Subtraction

Subtract 78 from 362 and then Subtract 9 from the result.

Solution : The vertical presentation of subtracting 78 from 362 is shown below.

362
78
-----
-----

3^{2}6^{15}2^{12}
78
----
284
----

Check : You may add 284 and 78 and check whether it is equal to 362 or not.

284
78
_{1}_{1}
---
362
---

It is verified to be correct.

Now we have to subtract 9 from the result, 284.

The vertical presentation of the process is shown below.

284
9
-----
-----

28^{7}4^{14}
9
----
275
----

Check : You may add 275 and 9 and check whether it is equal to 284 or not.

275
9
_{1}
---
284
---

It is verified to be correct.

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Subtract the second number from the first. Also, check your answer by doing the appropriate addition.

487, 398

630, 247

234, 97

300, 9

111, 88

934, 745

257, 8

107, 19

633, 155

816, 37

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