criss-cross multiplication.pdf

This is one of the fastest techniques of multiplication…

Helps you get the answer of any multiplication problem in just one line !

We will begin with multiplication of two-digit numbers

We will use the 3 steps that are given below:

A) * *

* *

B) * *

* *

C) * *

* *

Let us suppose we want to multiply:

2 3

x 1 2

We follow step (A) as seen before:

A) * *

* *

2 3

X 1 26

We get the answer as (3 x 2) equals 6.

We follow step (B) as seen before:

B) * *

* *

2 3

X 1 26

We cross-multiply and add. (2 x 2) + (1 x 3) is 7.

7

We follow step (C) as seen before:

A) * *

* *

2 3

X 1 26

We get the answer as (2 x 1) equals 2.

72

The final answer is 276

Another example…

Let us suppose we want to multiply:

3 4

x 1 1

We follow step (A) as seen before:

A) * *

* *

3 4

X 1 14

We get the answer as (4 x 1) equals 4.

We follow step (B) as seen before:

B) * *

* *

3 4

X 1 14

We cross-multiply and add. (3 x 1) + (4 x 1) is 7.

7

We follow step (C) as seen before:

A) * *

* *

3 4

X 1 14

We get the answer as (3 x 1) equals 3.

73

The final answer is 374

More Examples:

3 2 3 1 1 4

x 2 1 x 1 2 x 2 16 : 3+4 : 2 3 : 6+1 : 2 2 : 8 + 1 : 4

6 7 2 3 7 2 2 9 4

Two-digit Multiplication With Carry-over

Example:

4 4

x 2 2

Step (A) will be :

A) * *

* *

4 4

X 2 28

We get the answer as (4 x 2) equals 8.

Step (B) will be:

B) * *

* *

4 4

X 2 28

We cross-multiply and add. (4 x 2) + (4 x 2) is 16. We write 6 and carry-over 1.

6

1

Step (C) will be:

A) * *

* *

4 4

X 2 28

We multiply (4 x 2) and get 8. We add the 1 carried over and get the final answer as 9

69

3-digit MultiplicationWe will use the 5 steps that are given below:a) * * *

* * *

b) * * *

* * *

c) * * *

* * *

d) * * *

* * *

e) * * *

* * *

Step (A) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (2 x 1) equals 2.

Step (B) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (0 x 1) + (2 x 2) equals 4.

4

Step (C) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (3 x 1) + (0 x 2) + (2 x 1) equals 5.

45

Step (D) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (3 x 2) + (1 x 0) equals 6.

456

Step (E) will be :

A) * * *

* * *

3 0 2

X 1 2 12

We get the answer as (3 x 1) equals 3.

4563

Three-digit Multiplication With Carry-over

5 0 2

x 1 6 1

Example:

Step (A) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (2 x 1) equals 2.

Step (B) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (0 x 1) + (6 x 2) equals 12. We write 2 and carry-over 1.

2

1

Step (C) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (5 x 1) + (0 x 6) + (2 x 1) equals 7…(plus 1 carried over) equals 8

28

1

Step (D) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (6 x 5) + (1 x 0) equals 30. We write 0 and carry-over 3.

280

3

Step (E) will be :

A) * * *

* * *

5 0 2

X 1 6 12

We get the answer as (5 x 1) equals 5. We add to it the 3 carried over. The final answer is 8.

2808

3

More Examples:

3 4 2 3 6 1 7 1 4

x 2 0 1 x 1 4 2 x 9 3 5

68742 51262 667590

Let us have a look at the steps used in multiplication of four digit numbers…

4-digit MultiplicationWe will use the 7 steps that are given below:a) * * * *

* * * *

b) * * * *

* * * *

c) * * * *

* * * *

d) * * * *

* * * *

e) * * * *

* * * *

f) * * * *

* * * *

g) * * * *

* * * *

In this way, we can go on and multiply 5-digit, 6-digit, 7-digit and bigger numbers

But rather than doing examples of every type, I will give you a simple formula that you can use for all such numbers.

By learning the formula, you will be able to do any multiplication problem.

FORMULA

The number of steps to be used in any multiplication technique can be found out by using the formula

‘2 x (number of digits) – 1’

• Thus, when we multiplied 2-digit numbers, the steps used are

2 x 2 – 1 = 3

• When we multiply 3-digit numbers, the steps used are 2 x 3 – 1 = 5

• When we multiply 4-digit numbers, the steps used are

2 x 4 – 1 = 7

Just go a few slides back and carefully observe the notation of steps used in 2-digit, 3-digit and 4-digit numbers.

They follow a particular trend..

You can expand the same trend to multiply higher order numbers..