Division: Dividing Fast!

 

This video will teach you how to divide any number by 9.

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!

                                                                          

                                                                          
                                                        

                                                                                  

Division: Divisibility Rules

Have you ever wondered if 198676 is divisible by 3, but you don't want to do the math to figure it out? Well, there is a way to do this, and it is by using the Divisibility Rules. The divisibility rules are rules that tell you if a number (x) can be divided by certain number or not. For example if you didn't know if 26 can be divided by 2 or not, just check the divisibility rule for 2:

 The last digit must be divisible by 2, or be even.

Using that divisibility rule, you can apply that rule to the number to see if its divisible by 2 or not (which it is).  Here are the list of divisibility rules from 2-12:

Divisibility Rules

Rule for 2: The last digit must be divisible by 2 or be even.

Rule for 3: The sum of the digits must be divisible by 3.

Rule for 4: The last two digits must be divisible by 4.

                   (Example: 536 is divisible by 4 because 36 is divisible by 4)

Rule for 5: The last digit must be 0 or 5.

Rule for 6: The number must be even and divisible by 3.

Rule for 7: The number must be broken down into numbers that are both divisible by 7.

Rule for 8: The last three digits must be divisible by 8.

Rule for 9: The sum of the digits must be a multiple of 9.

Rule for 10: The last digit must be 0.

Rule for 11: The difference of the sum of odd-placed digits and the sum of the even-placed digits of the number must be 11 or 0. Let me explain:


Example: 139271


The bolded digits are odd placed digits. This is because if you were to count from right to left, 1 is the first digit from the right side, 2 is the third digit from the right side, and 3 is the fifth digit from the right side. 


As you notice each of those numbers are an odd number of digits from the right side. That is why they're odd placed digits. This also goes with the evens. 


Rule for 12: The number must be divisible by 3 and 4.

I think you might be able to find the pattern in the divisibility rules and use them to make rules for all the numbers. I hope this helped! 

                         

Multiplication: Nine Times Table At Your Fingertips

Having trouble remembering the 9x table? The answers are literally at your fingertips! Using the Fingertip Method, I will teach you how to remember the 9x table with no trouble at all!