Power

# The power of the number nine – is it just magic or is it real

Most people don’t realize the full power of the number nine. First, it is the largest single number in the ten number system. The numbers of the ten number system are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. This may not sound like much but it is the magic of the nine times multiplication table. For each product of the nine multiplication table, the sum of the digits in the product is nine. Let’s go down the list. 9 times 1 equals 9, 9 times 2 equals 18, 9 times 3 equals 27, and so on for 36, 45, 54, 63, 72, 81, and 90. When we add the numbers of the product, such as 27, the sum adds up to nine, i.e. 2 + 7 = 9. Now let’s expand this thought. Can it be said that a number is equally divisible by 9 if the digits of that number add up to nine? What about 673218? Numbers add up to 27, which add up to 9. The answer to 673218 divided by 9 is even 74802. Does this work every time? It seems so. Is there an algebraic expression that explains this phenomenon? If this is true, then there will be evidence or theory to explain this. Do we need this to use it? of course not!

Can we use magic 9 to check large multiplication problems like 459 by 2322? 459 times 2322 equals 1,065,798. The sum of the digits of 459 is 18, which is 9. The sum of the digits of 2322 is 9. The sum of the digits of 1,065,798 is 36, which is 9.
Does this prove that 459 times 2322 equals 1,065,798? No, but she tells us it’s not wrong. What I mean is that if the sum of your answer number is not 9, you will know that your answer was wrong.

Well, that’s all well and good if your numbers are such that their digits go to nine, but what about the rest of the number, the ones that don’t go to nine? Can magic threads help me no matter what numbers i am multiple? You bet you can! In this case, we pay attention to a number called the remainder 9. Let’s take 76 times 23 which equals 1748. The sum of the digits in 76 is 13, and their sum again is 4. Hence the 9s remainder of 76 is 4. The sum of the number 23 is 5. This makes the remaining 5 9s of 23. At this point, multiply the two remainders of the 9s, that is 4 by 5, which equals 20 the number of digits we add to 2. This is the sum of the 9s that we add up again. Try it out for yourself with your own multiplication problems worksheet.