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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’s the largest single digit in the base ten number system. The digits of the base ten number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. That may not seem like much but it is magic for the nine’s multiplication table. For every product of the nine multiplication table, the sum of the digits in the product adds up to nine. Let’s go down the list. 9 times 1 is equal to 9, 9 times 2 is equal to 18, 9 times 3 is equal to 27, and so on for 36, 45, 54, 63, 72, 81, and 90. When we add the digits of the product, such as 27, the sum adds up to nine, i.e. 2 + 7 = 9. Now let’s extend that thought. Could it be said that a number is evenly divisible by 9 if the digits of that number added up to nine? How about 673218? The digits add up to 27, which add up to 9. Answer to 673218 divided by 9 is 74802 even. Does this work every time? It appears so. Is there an algebraic expression that could explain this phenomenon? If it’s true, there would be a proof or theorem which explains it. Do we need this, to use it? Of course not!
Can we use magic 9 to check large multiplication problems like 459 times 2322? The product of 459 times 2322 is 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 statement that the product of 459 times 2322 is equal to 1,065,798 is correct? No, but it does tell us that it is not wrong. What I mean is if your digit sum of your answer hadn’t been 9, then you would have known that your answer was wrong.
Well, this is all well and good if your numbers are such that their digits add up to nine, but what about the rest of the number, those that don’t add up to nine? Can magic nines help me regardless of what numbers I am multiple? You bet you it can! In this case we pay attention to a number called the 9s remainder. Let’s take 76 times 23 which is equal to 1748. The digit sum on 76 is 13, summed again is 4. Hence the 9s remainder for 76 is 4. The digit sum of 23 is 5. That makes 5 the 9s remainder of 23. At this point multiply the two 9s remainders, i.e. 4 times 5, which is equal to 20 whose digits add up to 2. This is the 9s remainder we are looking for when we sum the digits of 1748. Sure enough the digits add up to 20, summed again is 2. Try it yourself with your own worksheet of multiplication problems.
Let’s see how it can reveal a wrong answer. How about 337 times 8323? Could the answer be 2,804,861? It looks right but let’s apply our test. The digit sum of 337 is 13, summed again is 4. So the 9′s remainder of 337 is 4. The digit sum of 8323 is 16, summed again is 7. 4 times 7 is 28, which is 10, summed again is 1. The 9s remainder of our answer to 337 times 8323 must be 1. Now let’s sum the digits of 2,804,861, which is 29, which is 11, summed again is 2. This tells us that 2,804,861 is not the correct answer to 337 times 8323. And sure enough it isn’t. The correct answer is 2,804,851, whose digits add up to 28, which is 10, summed again is 1. Use caution here. This trick only reveals a wrong answer. It is no assurance of a correct answer. Know that the number 2,804,581 gives us the same digit sum as the number 2,804,851, yet we know that the latter is correct and the former is not. This trick is no guarantee that your answer is correct. It’s just a little assurance that your answer is not necessarily wrong.
Now for those who like to play with math and math concepts, the question is how much of this applies to the largest digit in any other base number systems. I know that the multiplies of 7 in the base 8 number system are 7, 16, 25, 34, 43, 52, 61, and 70 in base eight (See note below). All their digit sums add up to 7. We can define this in an algebraic equation; (b-1) *n = b*(n-1) + (b-n) where b is the base number and n is a digit between 0 and (b-1). So in the case of base ten, the equation is (10-1)*n = 10*(n-1)+(10-n). This solves to 9*n = 10n-10+10-n which is equal to 9*n is equal to 9n. I know this looks obvious, but in math, if you can get both side to solve out to the same expression that’s good. The equation (b-1)*n = b*(n-1) + (b-n) simplifies to (b-1)*n = b*n – b + b – n which is (b*n-n) which is equal to (b-1)*n. This tells us that the multiplies of the largest digit in any base number system acts the same as the multiplies of nine in the base ten number system. Whether the rest of it holds true too is up to you to discover. Welcome to the exciting world of mathematics.
Note: The number 16 in base eight is the product of 2 times 7 which is 14 in base ten. The 1 in the base 8 number 16 is in the 8s position. Hence 16 in base 8 is calculated in base ten as (1 * 
+ 6 = 8 + 6 = 14. Different base number systems are whole other area of mathematics worth investigating. Recalculate the other multiples of seven in base eight into base ten and verify them for yourself.
Power Point – 7 Barriers to Power Point Presentations That Your Audiences Don’t Hate
Do you automatically open your Power Point templates every time you get ready for a business presentation or speech? Power Point has become the medium of choice of speakers giving business presentations today yet most audiences will say they don’t like it.
Here are 7 common barriers to making your Power Point presentations work for your audiences and how to overcome them.
The starting point for every presentation you write is to ask the question: “What does the audience care about?” The answer must be about a pain or difficult situation they are facing and how you can help them face it. Once you know the answer, you can overcome the barriers to bad Power Point presentations.
#1) Too many bullets: You load your slides with bullets because you don’t want to forget something that the audience needs to know.
Solution: Be ruthless in examining whether they really need to know it all. They will not be tested on your content. Remember these sayings still apply: “less is more” and “a picture is worth a thousand words.”
#2) Bullets are too long: You write full sentences with two or three thoughts in each one.
Solution: Make your bullets short and comprised of only nouns and adjectives. “Highest quality help desk” says a lot more than “We offer highly trained help desk staff and the help desk is staffed 18 hours per day.”
#3) Complicated graphics: your graphics depict every detailed step you would talk about if you were training someone in the process.
Solution: Get way to up to 50,000 feet. Your audience will get the lay of the land. Then you spend your speaking time making the full story interesting and compelling and based on your expertise.
#4) Too much information: you are presenting not teaching
Solution: Go back to your answer to the question “What does the audience care about?” Then only give them the information that provides a solution to the thing they care about. No history or an overview or the background. Just the content that is narrowly focused on addressing their current problem or issue.
#5) Special effects: the IT folks who developed Power Point get their job satisfaction from creating more bells and whistles.
Solution: Special effects belong in movies not in your presentation. They force you to distort your expertise and ruin your ability to deliver a compelling presentation that works for your audience (see “What does your audience care about?”). Keep it simple-no builds, no flying text, just lots of white space surrounding your carefully thought out short list of short bullets.
#6) Hard to see: there’s a huge difference between what looks great on your computer and what projects well.
Solution: Use the tried and true rules of the road: fonts 12 point or larger; no italics; light text on dark background; large graphics and photos; non-custom colors.
#7) Badly presented: Even the best written power point deck can fail to move the audience if the presenter is poor.
Solution:
Speak only about what you know Double the amount of time you think you need to practice Do not use pointers. If you must call attention to something on the screen, gesture towards it with your hand. Remember: you are the presentation and the slide deck is your back up. Speak towards the audience and tell them what is important or interesting
#7.5) Using slides when you don’t need them: Not every bit of your spoken content needs to be covered by a slide.
Solution: Insert some blank blue slides into your deck at the places when you’re going to tell a story or use a prop or invite audience participation.
The Balance of Power Between Men and Women
In today’s society there is the common perception that women and men are equal. As human beings we are all equal, which means we should not maltreat one another. We must treat each other equally and with respect. However women and men are not equal in the spiritual law. God has chosen the man to be the leader and the woman the follower. As much as we may wish to dispute this, the word of the Lord surpasses all our arguments.
In the bible it is written that, ‘But I would have you know, that the head of every man is Christ; and the head of the woman is man; and the head of Christ is God.’ Further down this same passage it is written, ‘For the man is not of the woman; but the woman of the man. Neither was the man created for the woman but the woman for the man.’ Men would always remain the stronger gender despite our efforts to change this course, they are built physically that way to serve this purpose. We are sometimes mislead in our reasoning here when it comes to occupation. This teaching does not imply that women can’t do the job of a men. If she is physically built for it then she has every right to. However before God we must be humble enough to accept who he has decided to lead. As much as we search for a level of equality humanely we must also be aware that this is the spiritual aspect of our existence which we cannot deny. It is imperative that this is maintained for there to be a balance in our society.
Thus said, the bible also teaches us: ‘Nevertheless neither is the man without the woman, neither the woman without the man in the Lord. For as the woman is of the man; even so is the man also by the woman; but all things are of God.’ This means that men should not oppress women or vice versa as we are all children of God. It is important that this balance be maintained in society today for our development and growth both humanely and spiritually. Seeking equality in society between men and women should not overcome our existence. It should be built on the basis of respect with the knowledge that no matter how equal we may consider ourselves to be God has already chosen who to lead. Anything other than what God has said is man’s wisdom and not God’s.