Multiplication: "Odd" Theory

Here's an interesting theory I expanded on. I hope you like it! In order to do this trick however, you need to know your perfect squares.

If you want to know the answer to a multiplication problem such as:

                                                            11 x 19
This is how you do it with my theory:

Step 1: Identify the factors. In this case, it would be 11 and 19.
Step 2: Find the average of the factors. In this case, it would be 15.
Step 3: Calculate that number squared:


                                                            15 x 15= 225
Step 4: Increase one of the of the factors in this problem and decrease the other factor by 1. Then calculate it. It should look like this:


                                                            16 x 14 = 224

Note: If you noticed, the product of the first problem happens to be higher than the product of the second problem by 1. 225 - 224 = 1!

Step 5: Repeat Step 4. It should look like this:


                                                            17 x 13 = 221


Note: If you noticed, the product of the second problem happens to be higher than the product of the third problem by 3. 224 - 221 = 3!


Do you notice a pattern in the products? Let me show you: 

As you can see, each time you increase one of the factors by one and decrease the other by 1. The difference between the product of these 2 numbers and the product of the previous two numbers, increases one odd number higher. Using this theory, you will be able to widen your range in number of math facts!

11 x 19 = 209

Hope this helped!