TWO DIGIT MULTIPLICATION - LEARNING MADE EASY, EXAMPLES, EXERCISE

Learn/Teach
Multiplication through Fun Games
before Two Digit Multiplication
For details, see near
the bottom of this page.

Please study
Single Digit Multiplication,
if you have not already done so.

There, we explained multiplication
of a Multi-digit number by
a single digit number.

That knowledge is a prerequisite here.

Here, we deal with multiplication
by Two-Digit numbers.

Multiplication by a
two digit number

Here we do the multiplication by
single digit number in ones' place.

Then we do the multiplication by
single digit number in tens' place.

We write the second product
below the first product
starting from tens' place
and proceeding to the left.

The process will be clear
from the following examples
of Two Digit Multiplication.

Example 1 of
Two Digit Multiplication

Perform the Two Digit
Multiplication 97 x 86.

Solution :

          97
          86
        ----           4
          582        5
         776
        ----
        8342
        ----

7 x 6 gives 42. We write 2 in
units' place, and 4 at a distance.

9 x 6 gives 54. We add 4 to this 54
to get 58. 4 is striked off. 58 is
placed to the left of 2 to get 582.

Thus, 97 x 6 is done, as explained in
Single Digit Multiplication.
This gave 582.

Then we multiply 97 with 8.

7 x 8 gives 56. We write 6 in
tens' place. and 5 at a distance.

9 x 8 gives 72. We add 5 to this 72
to get 77. 5 is striked off. 77 is
placed to the left of 6 to get 776.

Thus 97 x 8 gave 776.

Note that 776 is written
below 582 with 6 at tens'
place and then to the left.

These 582 and 776 placed
properly, are added.

While adding, 2 is descended
in the units' place.

8 and 6 added in tens' place to get
14. We write 4 in tens' place and
carry over 1 to the hundreds' place.

We add 5 and 7 and the carried over
1 in hundreds' place to get 13.
We write 3 in hundreds' place and
carry over 1 to thousands' place.

7 and carried over 1 in thousands'
place added gives 8 and this 8
is placed in thousands' place.

Thus 97 x 86 = 8342.

Example 2 of
Two Digit Multiplication

Find 234 x 57

Solution :

          234
           57
        ----           2  2
         1638        2  1
        1170
        ----
        13338
        ----

4 x 7 gives 28. We write 8 in
units' place. and 2 at a distance.

3 x 7 gives 21. We add 2 to this
21 to get 23. 2 at a distance
is striked off. We write 3 in
tens' place and 2 at a distance.

2 x 7 gives 14. We add 2 to this
14 to get 16. 2 at a distance is
striked off. 16 is placed to the
left of 38 to get 1638.

Thus, 234 x 7 is done,
as explained in
Single Digit Multiplication.
This gave 1638.

Then we multiply 234 with 5.

4 x 5 gives 20. We write 0 in
tens' place. and 2 at a distance.

3 x 5 gives 15. We add 2 to
this 15 to get 17. 2 is striked
off. We write 7 in hundreds'
place and 1 at a distance.

2 x 5 gives 10. We add 1 to
this 10 to get 11. 1 is striked
off. 11 is placed to the left
of 70 to get 1170.

Thus 234 x 5 gave 1170.

Note that 1170 is written
below 1638 with 0 at tens'
place and then to the left.

These 1638 and 1170 placed
properly, are added.

While adding, 8 is descended
in the units' place.

3 and 0 added in tens' place to
get 3. we write 3 in tens' place.

We add 6 and 7 to get 13. We
write 3 in hundreds' place and
carry over 1 to thousands' place.

1 and 1 and carried over 1 in
thousands' place added gives 3 and
this 3 is placed in thousands' place.

1 is descended in ten thousands place.

Thus 234 x 57 = 13338.

Example 3 of
Two Digit Multiplication

Find 9182 x 43

Solution :

          9182
            43
        ------           2  
         27546        3  
        36728
        ------
        394826
        ------

Here, 2 x 3 gives 6.
We write 6 in units' place.

Next, 8 x 3 gives 24.
We write 4 in tens'
place and 2 at a distance.

Then, 1 x 3 gives 3. We
add 2 to this 3 to get 5.
Then 2 is striked off.
We write 5 in hundreds' place.

Then, 9 x 3 gives 27.
We write 27 to the left
of 546 already present.

Thus 9182 x 3 = 27546.

Then we multiply 9182 with 4.

Here, 2 x 4 gives 8.
We write 8 in tens' place.

Next, 8 x 4 gives 32.
We write 2 in hundreds'
place and 3 at a distance.

Then, 1 x 4 gives 4. We add
3 to this 4 to get 7. Then
3 is striked off. We write
7 in thousands' place.

Then, 9 x 4 gives 36. We
write 36 to the left
of 728 already present.

Thus 9182 x 4 gave 36728.

Note that 36728 is written
below 27546 with 8 at tens'
place and then to the left.

These 27546 and 36728
placed properly, are added.

While adding, 6 is descended
in the units' place.

4 and 8 added in tens' place to
get 12. We write 2 in tens' place
and carry over 1 to hundreds' place.

We add 5 and 2 in hundreds' place
and carried over 1 to get 8.
We write 8 in hundreds' place.

7 and 7 added in thousands'
place to get 14. We write 4 in
thousands' place and carry over
1 to ten thousands' place.

We add 2 and 6 in ten thousands
place and carried over 1 to get 9.
We write 9 in ten thousands place.

3 is descended in hundred thousands'
(one lakh's) place.

Thus 9182 x 43 = 394826.

Other Topics Of Multiplication

The following links take you
to other topics of multiplication.

Multiplying Two Digit Numbers
easily using Vedic math

multiplying by Three
or more digit numbers,

Multiplying Three Digit Numbers
easily using Vedic math

Multiplying Four Digit Numbers
easily using Vedic math

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Exercise on
Two Digit Multiplication

Do the following Two Digit Multiplications

1. 34 x 26
2. 78 x 17
3. 459 x 34
4. 691 x 29
5. 1247 x 48
6. 9673 x 54
7. 1234 x 96
8. 3759 x 52
9. 4829 x 28
10. 8302 x 71

For Answers see at the end of the page.

Answers to Exercise on
Two Digit Multiplication

Answers to problems on Two Digit Multiplication :

1. 884
2. 1326
3. 15606
4. 20039
5. 59856
6. 522342
7. 118464
8. 195468
9. 135212
10. 589442