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!

Addition: No Carrying!

How you ever thought in addition: "I don't want to carry over. Its so hard!" Well, I have a solution for that! Its called the no-carrying trick, and I'm to guide you step-by-step in the process on how to do it! Let me show you an example:

   129

+ 423

Now for those of you, who can do can't do mental math, you're all probably wondering: "How can I do this problem without carrying over?" So let me show you the step by step process:

Step 1: Look at the place values farthest on the left. In this case, it would be 4 and 1. 
Step 2: Find their true values. For example, since 4 and 1 are in the hundred's place, their true values are 400 and 100.
Step 3: Find out the sum of the 2 numbers. Then put the answer below. Make sure its aligned correctly:

                                                                                 129

                                                                            +   423

                                                                                 500

Step 4: Now move over one place value to the right (In this case, since we started with the hundreds place, moving one place value to the right will get us to the tens place).

Step 5: Look at the place value you are on now. Repeat Step 2 and Step 3. Make sure its aligned correctly:

                                                                               129

                                                                           +  423

                                                                               500

                                                                                 40


Step 6: Repeat Step 4 and Step 5 for the ones place (in this example). You will notice that the sum for the ones digits place is 12. So how can you fit it in? The answer is simple, simply move the tens digit of the number (in 12, 1 is the 10s digit) one place value to the left. The result should look like this:


                                                                               129
                                                                          +   423 
                                                                               500
                                                                                 40
                                                                                 12


Step 7: Add the "solution numbers" together for you to get the solution of the entire problem. It should look like this:

                                                                               129

                                                                           +  423

                                                                               500
                                                                                 40             
                                                                           +    12
                                                                               552



It may seem confusing now, but once you get it, you'll be able to use this method in your head for various problems!