3 DIGIT SUBTRACTION MADE EASY WITH EXAMPLES, EXERCISE

Learn/Teach
Subtraction through Fun Games
before 3 digit Subtraction
For details, see near
the bottom of this page.

Please study
Subtraction Table,
if you have not already done so.

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.

          1009010
              1
          ----
            99
          ----

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.

Let us see examples on
3 Digit Subtraction.

Example 1 of 3 Digit Subtraction

Subtract 189 from 725.

Solution :
The vertical presentation of
the problem is shown below.

          725
          189
          -----

          -----

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.

          76211515
            189
          ----
           536
          ----

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
          ---

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
          -----

          -----

32615212
   78
----
 284
----

          284
           78
           1
          1
          ---
          362
          ---

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

The vertical presentation of
the process is shown below.

          284
            9
          -----

          -----

          287414
              9
          ----
           275
          ----

          275
            9
           1
          ---
          284
          ---

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Exercise on 3 Digit Subtraction

Problems on 3 Digit Subtraction :

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

1. 487, 398
2. 630, 247
3. 234, 97
4. 300, 9
5. 111, 88
6. 934, 745
7. 257, 8
8. 107, 19
9. 633, 155
10. 816, 37

For Answers, see at the end of the page.

Answers to Exercise on 3 Digit Subtraction

Answers to the problems on 3 Digit Subtraction :

1. 89
2. 383
3. 137
4. 291
5. 23
6. 189
7. 249
8. 88
9. 478
10. 779