First we need to know what a duplex number is. Numbers like 11, 22, 33, 44 etc, with repeated digits, are called duplex numbers. We already know how to multiply by 11. Here we are going to learn a similar method for other duplex numbers.
Multiplication by 22
Step 1: First multiply the units digit by 2.
Step 2: Add the units and the tens digit and multiply by 2.
Step 3: Multiply the tens digit by 2.
Example: 34 X 22
Step 1
4 x 2 = 8
Step 2
3 + 4 = 7
7 x 2 = 14
Step 3
3 x 2 = 6
So we have: 6 14 8
8 will be the units digit of the answer, 4 will be the tens digit with the 1 carried over and added to 6 to make 7 the hundreds digit.
Answer: 748
We use the same method to multiply by 33. The difference is that we multiply the numbers by 3. Let us see that with an example.
Example: 46 x 33
Step 1
6 x 3 = 18
Step 2
6 + 4 = 10
10 x 3 = 30
Step 3
4 x 3 = 12
So we have: 12 30 1 8
8 will be the units digit of the answer, 1 is carried over and added to 30 so 1 will be the tens digit, 3 is carried over and added to 12 to make 15 the first part of the answer
Answer: 1518
Now let us look at multiplying by 66
Example : 28 X 66
Step 1
8 x 6 = 48
Step 2
2 + 8 = 10
10 x 6 = 60
Step 3
2 x 6 = 12
So we have: 12 60 48
8 will be the units digit of the answer, 4 is carried over and added to 60 so 4 will be the tens digit, 6 is carried over and added to 12 to make 18 the first part of the answer
Answer: 1848
The same method can be used for all the duplex numbers. With practice, we can calculate mentally and arrive at the answer.