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.

Click image to enlarge

**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.

So, the final product is 408.

This strategy can also be done horizontally. The image below show the steps in multiplying 17 and 43. You may click the image to make it larger.

Click image to enlarge

**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.

*Related*

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