The usual steps that we in multiplying 2 digit numbers is to multiply vertically as shown in the first figure. We first use the digits ones digit of the multiplicand (12) and distribute to the ones and tens digit of the multiplier (34) shown in Step 1 and Step 2 and write the products. Then, we multiply the tens digit of the multiplicand to the ones and tens digit of the multiplier (Steps 3 and 4). Finally, we add the products to get the final answer.
As you can see, this method requires 5 steps. The discussion below is about an alternative method.
The Math Shortcut
Below are the steps for the modified method in multiplying 34 and 12. With enough practice, I think this method will make you multiply faster.
Step 1: Multiply 2 and 4. This gives a product of 8. Write 8 as ones digit of the final answer.
Step 2: Multiply 3 and 2, multiply 1 and 4, and add the products. This results to 10. Write 0 as the tens digit of the final answer and take note of 1 which will be the carry over to the the hundreds digit of the final answer.
Step 3: Multiply 1 and 3 and add the carry over from Step 2. This gives 4. Write 4 in the hundreds digit of the final answer.
Generalizing the Shortcut
From the examples above, we can say that if we have a number ab and cd where a, b, c, and d are digits, and we want to multiply ab × cd, the following is the steps can be done.
Step 1: b × d
Note: If the product is more than 10, carry over 1 and add to the final answer in Step 2.
Step 2: a × d + b × c
Note: If the sum is more than 10, carry over 1 and add to the final answer in Step 3.
Step 3: a × c.
The results in the calculation in Step 1, Step 2, and Step 3 are the ones, tens, and hundreds digits of the product respectively.