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

There, we introduced multiplication as
repeated addition and solved a number
of examples including word problems.

Also, the need of multiplication tables
and doing multiplication with the help
of tables was introduced.

A number of solved examples on
multiplication of two digit numbers by a
single digit number were lucidly explained.

That knowledge is a prerequisite here.

Here, we extend the topic by giving
more examples. We also explain
multiplication of three or four digit
numbers with a single digit number,
by a number of solved examples.

This presentation is ok for learning
multiplication of single digit number
with two digit number.

However when multiplying a multi-digit
number with a multi-digit number,
multiplication with single-digit
number is a small part of it and we may
have to present it in a single line.

Let us present the above
example 87 x 9 in a single line.

^{6}
87
9
---
783
---

Here, in the value of 7 x 9 (= 63 ),
3 is presented in units' place
and 6 is presented above in tens'
place in small letter.

8 x 9 gave 72 and 6 is added to it
to get 78 and this 78 is presented
to the left side of 3 to get 783.

Later we don't even write small 6 above,
as written here. We write it else where
and rub it off after adding it to 72.

87
9
--- ^{6}
783
---

See small 6 written at a distance. It
is striked off after adding it to 72.

Let us see one more example with this simplified presentation.

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Here, 6 x 9 gives 54. We write 4
in units' place and 5 at a distance.

Next, 8 x 9 gives 72. We add 5 to
this 72 to make it 77. Then 5 is
striked off. We write 7 in tens'
place and 7 at a distance.

Then, 7 x 9 gives 63. We add 7 to
this 63 to get 70. Then 7 at a
distance is striked off. We write
70 to the left of 74 already present.

Thus 786 x 9 = 7074. Ans.

Example 5 of Multiplication Problems

Find 1983 x 7

Solution :

1983
7
----- ^{2}^{5}^{6}
13881
-----

Here, 3 x 7 gives 21. We write 1
in units' place and 2 at a distance.

Next, 8 x 7 gives 56. We add 2 to
this 56 to make it 58. Then 2 is
striked off. We write 8 in tens'
place and 5 at a distance.

Then, 9 x 7 gives 63. We add 5 to
this 63 to get 68. Then 5 is striked
off. We write 8 in hundreds' place
and 6 at a distance.

Then, 1 x 7 gives 7. We add 6 to this
7 to get 13. Then 6 is striked off. We
write 13 to the left of 881 already present.

Thus 1983 x 7 = 13881. Ans.

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Exercise on Multiplication Problems

Solve the following Multiplication Problems

23 x 6

67 x 8

189 x 7

987 x 9

2367 x 4

254 x 3

9876 x 2

4567 x 8

3456 x 9

2345 x 5

For Answers see at the end of the page.

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