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# Column Multiplication

We know that multiplication of two Numbers can be done by repeated addition, when the two numbers are smaller. In case we come across the bigger numbers, we are not able to get the result by simple addition. Thus we use column method to get the product of the given numbers.

In column multiplication, when we have two numbers say 124 X 35. Here we first multiply 12 by 5, i.e. the digit at ones place and then multiply 124 by 1 tens(10) . Finally the two products are added up to get the product. The column multiplication method is explained by an example in the following steps:

Step 1: Here, we multiply  124 by 5

Step 2: Here, 2 from ones place is carried to tens place and it becomes

Step 3: Here, 1 is from tens place is carried to hundreds place and it becomes

Step 4: Here we multiply 124 by 30 and for this just multiply 124 by 3 and put 0 at ones place

Step 5: Here, 1 from ones place is carried to  tens place and it becomes

Step 6: 124 X 30 = 3720

Step 7: 3720 + 620 = 4340

Finally we get the result as 124 X 35 = 4340

## Find the product of 2008 and 24?

First we write the Numbers at their proper places
Thousands        hundreds            tens     ones
2                      0                       0          8
X                     2           4
__________________________________________ In first step we multiply 2 0 0 8 by 4, we get
8                      0                        3             2 Now in next step, we first place X at ones place and then multiply 2 0 0 8 by 4, for this we start writing the result from tens     place and not from ones place. The two results are then added

Thousands        hundreds            tens     ones
2                      0                       0          8
X                     2           4
__________________________________________
8                      0                        3             2
40                      1                         6            X
___________________________________________ Now the two rows are added to get the product of 2 0 0 8 by 2 4
4 8                     1                          9           2
= 48192.

## Find the product of 125 * 52?

We arrange the given Numbers at their proper place and then perform Column Multiplication. For this in first row 125 is multiplied by 2 and 125 is multiplied by 5 at tens place.

hundreds           tens          ones
1                   2                5
X                    5               2
_______________________________
1                    4                10,
When we multiply 2 X 5 at ones place , we get 10, from 10, 0 is retained at ones place and 1 is carried to tens place as a carry to be added

hundreds           tens          ones
1                   2                5
X                    5               2
_______________________________
1                     5               0
Now put X on ones place, multiply 125 by 5 and start writing the result from tens place.

hundreds           tens          ones
1                   2                5
X                    5               2
_______________________________
1                    5                0
5      10                 25                X
Here 2 from 25 is carried over and 1 from 10 at hundreds place is carried over. So above equation becomes:

hundreds           tens          ones
1                   2                5
X                    5               2
_______________________________
1        1                    5                0
5       0                     5                X Digits expressed in bold are carry over’s. Now the two rows are added to get the result
_______________________________
6         5                   0                0
_______________________________

## Multiply 500 by 12?

First we arrange the number on the place value table and then multiply 500 by 2 and 500 by 1 separately. We get
Hundreds             tens             ones
5                      0                  0
X                        1                 2
___________________________________
10                        0                     0,
Now in next step, we write X on ones place and proceed to multiply 500 by 1. We get:

Hundreds             tens             ones
5                      0                  0
X                        1                 2
___________________________________
10                        0                     0
50                        0                      X       Now we proceed, to add the two rows and get the result.
______________________________________
60                          0                      0
______________________________________

## Multiply 170 X 80?

This problem can be solved by simply multiplying 17 X 8 and then multiply it by 100
We get
tens      ones
1           7
X           8
________________
8           56
Now from 56, we take 5 to tens place and add it with 8, we get:

tens      ones
1           7
X           8
________________
13           6
________________
So multiplying 136 by 100 we get 13600.

## Find the product of 650 and 11?

Multiply 650 by 1, then multiply 650 by 10 and add the result
So we get:
Hundred    tens   ones
6               5        0
X                         1
___________________
6                5         0
___________________
On multiplying 650 by 10 we get 6500,
To get the result we add
6      5      0
+ 6   5      0     0
______________
7   1      5      0
______________

## Multiply 56 X 34?

In this question we first arrange the digits at their place

tens      ones
5           6
X     3           4
______________
20           24, Here 2 from 24 is carried to tens place and it becomes,
tens      ones
5           6
X     3           4
______________
2  2           4, Now put X at ones place in next row and multiply 56 X 3,
1  6  8           X
____________________  On adding the two rows we get the required result,
1  9   0         4
____________________

## Multiply 450 X 25?

First we arrange the digits at proper place and then proceed:

Hundreds     tens      ones
4                5            0
X                2            5
____________________________
20            25             0    from 25 of tens place, 2 is carried to hundreds place, we get
And get:

Hundreds     tens      ones
4                5            0
X                2            5
____________________________
22               5            0 ,   Now we place X at once place  and then multiply 450 by 2, we get

Hundreds     tens      ones
4                5            0
X                2            5
____________________________
22               5            0 ,
9 0              0            X
___________________________
11 2              5            0
___________________________

## Multiply 800 by 17?

Hundred   tens  ones
8              0       0
X              1       7
_______________________
56               0       0, we put X at ones place and then multiply 800 by 1, we get

Hundred   tens  ones
8              0       0
X              1       7
_______________________
56               0       0
8 0              0       X Now we add the two rows and get the result
______________________
13  6              0        0
________________________

## Multiply 345 by 200?

In such problems we can write them as
345 * 2 * 100,
So first we solve 345 * 2
Write the digits as per their place value and then multiply:

Hundreds    Tens    Ones
3               4         5
X                          2
______________________
6                 8         10, from 10, 0 retains the ones value and 1 is carried over to tens place,
We get,
Hundreds    Tens    Ones
3               4         5
X                          2
______________________
6                 9           0
______________________
Now we multiply 690 by 100,
= 690 * 100,
= 69000.

## Multiply 6009 by 1?

In such cases, we need not to apply column method to get the solution to this.
As any number is multiplied by 1, the result is same number. This property is called the Identity Property of Multiplication.
So we get:
= 6009 * 1,
= 6009.