# MULTIPLICATION PROBLEMS - SOLVING MADE EASY, EXAMPLES, EXERCISES

Learn/Teach
Multiplication Problems
through Fun Games

For details, see near

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.

Other Multiplication Problems
are covered in

multiplication by Two digit numbers,

Multiplying Two Digit Numbers
easily using Vedic math

multiplication by Three
or more digit numbers,

Multiplying Three Digit Numbers
easily using Vedic math

Multiplying Four Digit Numbers
easily using Vedic math

multiplication word problems.

### Example 1 of Multiplication Problems

Find 87 x 9.

Solution :

```          87
9
---
6
3
72
---
783
---
```

Thus 87 x 9 = 783.

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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### Example 2 of Multiplication Problems

Find 96 x 4

Solution :

```          96
4
---           2
384
---
```

Here 6 x 4 gave 24.
We write 4 in units' place
and 2 at a distance.

9 x 4 gave 36. We add 2
which is at a distance
(carried over from the result
of units' place multiplication).

This gives 38. Now, we strike
off the 2. We present this
38 before 4 to get 384.

Thus 96 x 4 = 384.

One last example in this category.

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### Example 3 of Multiplication Problems

Find 79 x 8.

Solution :

```          79
8
---           7
632
---
```

Thus 79 x 8 = 632.

Next Two Examples will be on
Multiplication of a three or four
digit number by a single digit number.

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### Example 4 of Multiplication Problems

Find 786 x 9

Solution :

```          786
9
----        5  7
7074
----
```

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

1. 23 x 6
2. 67 x 8
3. 189 x 7
4. 987 x 9
5. 2367 x 4
6. 254 x 3
7. 9876 x 2
8. 4567 x 8
9. 3456 x 9
10. 2345 x 5

For Answers see at the end of the page.

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