SUBTRACTION PROBLEMS MADE EASY WITH EXAMPLE, EXERCISE

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

Please study Subtraction Problems

on single digit numbers,

on Two Digit Numbers

on Three Digit Numbers,

if you have not already done so.

That knowledge is a prerequisite here.

Here, we deal with four digit numbers.

Subtraction of four digit numbers

We have already seen in
decimal number system
that the successor to 999 is 1000.
or the predecessor to 1000 is 999.

i.e. 1000 - 1 = 999.

Let us present the process in the
vertical presentation by using the
borrow method (also called
regrouping method) explained in

Two Digit Subtraction,

and applied in

3 Digit Subtraction.

100909010
     1
------
   999
------

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.

Similarly, in hundreds' place, we
have to descend the 9 since there is
nothing to subtract in hundreds' place.

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

So the answer is 999.

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

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

Thus 1000 - 1 = 999. Ans.

We also saw in the
decimal number system,
that the four digit numbers
range from 1000 to 9999.

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

In Subtraction Problems on four
digit numbers, this borrowing
will go one place further.

Let us see an example on
Subtraction Problem of
four Digit numbers.

Example on Subtraction Problems

Subtract 1987 from 5673.

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

          5673
          1987
          ----

          ----

          54615716313
            1987
          -------
           3686
          -------

i.e. we have to subtract 7 from 3.
But 7 is bigger than 3.

So, we have to borrow one (one10)
from the digit in tens' place i.e. 7.

Because of this borrowing, 3 in
units' place becomes 13 and 7
in tens' place becomes 6.

Now subtract 7 from 13 which
gives 6 in the units' place.

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

i.e. we have to subtract 8 from 6.
But 8 is bigger than 6.

So, we have to borrow one (one10)
from the digit in hundreds' place i.e. 6.

Because of this borrowing,
6 in tens' place becomes 16,
and 6 in hundreds' place becomes 5.

Now subtract 8 from 16 which
gives 8 in the tens' place.

Now, we have to subtract bottom
digit in the hundreds' place
from the new upper digit in
the hundreds' 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 thousands' place i.e. 5.

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
Thousands' place to the Hundreds' place.

Because of this borrowing, 5 in
hundreds' place becomes 15 and 5
in thousands' place becomes 4.

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

Now subtract 1 from 4 which
gives 3 in the thousands' place.

So the answer is 3686.

This process is shown in the
vertical presentation above.

See 3 in the units' place
is sriked off to become 13,

and 7 in the tens' place
is sriked off to become 16,

6 in the hundreds' place
is sriked off to become 15,

5 in the thousands' place
is sriked off to become 4.

Thus 5673 - 1987 = 3686. Ans.

Check :
You may add 3686 and 1987 and check
whether it is equal to 5673 or not.

          3686
          1987
            1
           1
          1
          ----
          5673
          ----

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Exercise on Subtraction Problems

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

1. 3296, 1254
2. 8785, 5897
3. 7012, 623
4. 2314, 98
5. 6300, 7
6. 1101, 865
7. 3034, 1657
8. 1107, 99
9. 6733, 4
10. 8000, 1111

For Answers, see at the end of the page.

Answers to Exercise on Subtraction Problems

Answers to the Subtraction Problems :

1. 2042
2. 2888
3. 6389
4. 2216
5. 6293
6. 236
7. 1377
8. 1008
9. 6729
10. 6889