Basics of Multiplications | Multiplication Tricks | Multiplication of Two Consecutive Numbers

Want to speed up in Multiplying two consecutive numbers ?

Before learning the Short Cut Method to multiply two consecutive numbers, let us take a look at the Traditional Method to calculate the results.

For Ex.  - 21 × 22

Step 1 :- We multiply 21 by 2 which is 42 

Step 2 :- Then we write unitary digit i.e 2 at result and we then take carry Tens digit of the obtained result  i.e. 4 

Step 3 :- Again we multiply 21 by 2 and which results 42 again add the Tens digit we have carried which can be calculated as 42 + 4 = 46 

Final Result - We get 462.

Now we will do the same problem by Short Cut Method.

This can be done in two ways. 

 Way 1 - Add 21 to the square of 21. (21 + 441 = 462)

OR 

 Way 2 - Subtract 22 from square of 22. (484 - 22 = 462)  

Let us understand the logic behind this method.

Logic - 

The product m × n can be written as 'n' times addition of 'm' .

 Let us try the same example with above logic.

For Way 1 

Step 1 :- First we will multiply 21 × 21 which is 441.

Step 2 :- Secondly, we will multiply 21 × 1 which results 21

Step 3 :- Add both the results. 441 + 21 =  462.

Final Result - We get 462.

For Way 2

Step 1 :- First we will multiply 22 × 22 which is 484.

Step 2 :- Secondly, we will multiply 22 × 1 which results 22

Step 3 :- Subtract 22 from 484. (484 - 22 =  462.)

Final Result - We get 462. 

Problems for Practice

1) 18 × 19

1) 33 × 34 

1) 45 × 46 

1) 28 × 29 

1) 36 × 37