Multiplication by duplex numbers
Happy New Year! It’s good to be back with you after the break. Let us start the new year with something interesting and exciting! Our topic today is multiplication by duplex numbers. Numbers like 11, 22, 33, 44 are called duplex numbers. We already know the easy method to multiply by 11, so we are going to learn a similar method for other duplex numbers, where we get the answer in a single step.
For multiplication by 11 we add neighbouring digits to get the answer. Let us recollect the method using an example.
To multiply 43 x 11
We put down 3 as the units digit of the answer.
Then add the two digits (4+3) and put the sum as the tens digit.
Put 4 as the hundreds digit.
The answer is 473.
We can practise this method so that we can do the problem mentally and get the answer in a single step.
Let us look at the steps for multiplication by 22.
Step 1: Multiply the units digit by 2; that will give you the units digit of the answer.
Step 2: Add the units and tens digits and multiply by 2. This will be the next digit.
Step 3: Multiply the tens digit by 2.
Let us see an example.
24 x 22
Step 1: 4 x 2 = 8. That is the units digit of the answer.
Step 2: (2 + 4) x 2 = 12. 2 is the tens digit of the answer and 1 is carried over.
Step 3: 2 x 2 = 4. 4 + 1(carried over) = 5
When multiplying by 11, we only add the digits in step 2, but for all other duplex numbers, we add and then multiply by the digit of the duplex number.
The same method can be used to multiply by 33. However, here we multiply by 3.
Let us see that with an example.
46 x 33
Step 1: 6 x 3 = 18. 8 is the units digit of the answer. 1 is carried.
Step 2: (4 + 6) x 2 = 30 +1(carried over) = 31. 1 is the tens digit of the answer and 3 is carried over.
Step 3: 4 x 3 = 12 + 3(carried over) = 15
It is easy and effortless to multiply any duplex number and get the answer in a single step.
You can try:
12 x 22; 15 x 22; 36 x 11; 42 x 33; 31 x 33