Lesson: Don’t just rush in and multiply. Look for simplification tricks first and you’ll be faster and more able to do math in your head.

The 11 Rule

Multiplying by 10 is easy enough, but multiplying by 11 in your head is a bit more of a challenge. If you don’t know the rules. All you do is separate a two digit number multiplied by 11 and add the sum of those two in-between.

For this example we’ll use 72.

• The first thing you want to do is separate the two digits, leaving a space between them.

• The only other step is to add the two digits together, in this case 7+2=9, and put that number between the other two.

• That’s it! 11 x 72= 792

• One more thing, if the sum of the two digits adds up to more than 10, say with 77, all you need to do is carry the 1 to the left.

• For 77, the 1 of 7+7=14 carries to make 11 x 77 = 847, not 747

The 11 Rule Continued

In addition to multiplying two digit numbers, there is another method to multiply *any* number by 11.
By adding each number with its ‘neighbor’ on the right, it acts the same as multiplying the entire number.

• Lets start with the number 2340897. First step, add a zero before it, making 02340897.

• The rest of the equation follows the same pattern, of adding the neighbor number to the right.

• For the 7, there’s nothing to the right, so just put down the 7.

• In the tens spot to the left, add the 9 to the neighbor, 7. Write down the 6, and carry the 1 on to the next step.

• Repeat this process for all the remaining units. Add 8 with its neighbor 9, plus one carried, to make 18. keep the 8, carry the 1.

• Add 0 with its neighbor 8, plus one carried, to make 9.

• Add 4 with its neighbor 0, and write it down.

• Add 3 with its neighbor 4, and mark down 7.

• Add 2 with its neighbor 3, and mark down 5.

• Finally for the last digit, you’ll add the 0 on the left with the first digit, 2.

• Put all of these together, and you will have 11 x 2340897, which totals 25,749,867.

You can directly write down the answer to any number multiplied by 11.

The 12 Rule

Almost identical to the previous rule, the 12 rule is very simple once you figure it out.
The primary difference between these two is that before you add numbers with their neighbor, you multiply it by two. *That’s it.*

• Lets use another random number, 6711273, as our example. Again, add a zero to the start to simplify. 06711273

• Next, we’ll follow the same neighbor to the right rule, but this time doubling the first number.

• To start, double the 3 on the far right, to get 6.

• Next, double the 7 and add the 3 to the right. This gives 17, so keep the 7 and carry the 1.

• Continue by doubling 2 and adding the 7, as well as the carried 1. This gives 12, keep 2 and carry 1.

• Next double 1, add two, and one carried, for 5.

• Double 1 again, add one, to make 3.

• Double 7 this time, and add the neighbor 1, for 15, or 5 with 1 carried.

• Now double 6, add 7, and the one carried, for 20. Carry the 2, mark the 0.

• Finally, the 0 doubled is still 0, plus neighbor 6 and carried 2 makes 8.

• Add up all of these and you get 80,535,276, which is 6711273 times 12.

In this game you and the computer opponent take turns moving the slider arrows above and below the numbers one through nine. When both sliders are picked, the number that those make multiplied together is taken on the board. Then the game continues with each player moving one of the two sliders every turn. The first person to line up four of the answers anywhere on the board wins.

Multiplication Game

Enjoy!

Three people check into a hotel. They pay $30 to the manager and go to their room. The manager suddenly remembers that the room rate is $25 and gives $5 to the bellboy to return to the people. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid $9 each, totalling $27. The bellboy has $2, totalling $29. Where is the missing $1?
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SOLUTION: (no cheating now…)
The solution to this problem is that the numbers have been added incorrectly. The question misleads you by adding the bellboy’s two dollars to the $27 paid, when really those two dollars are part of the $27. In the end, the Manager has $25 for the room, and the bellboy has $2 of the $27 dollars the men now have paid.

Kakuro

Some of you may have seen this optical illusion before. It appears to be a triangle made up of four parts, that when rearranged create an extra hole that shouldn’t be there. I’ve seen all sorts of ridiculous explanations (see the comments) on different websites, but it is in fact VERY simple. Look at the two triangles within the larger one. The smaller of the two triangles, the blue one, has a slope of .4, or 2/5. Now look at the red one. It has a slope of 3/8, which is .375, not the same slope as the other triangle. This means that off the bat, THIS IS NOT A TRIANGLE. It’s a quadrilateral. You can tell if you look closely that they are not in fact straight. This sort of makes the rest of the illusion moot, because it’s trying to convince you that it’s a triangle. They don’t specifically say that it is a triangle, but they call it figure ABC, when it really is figure ABCD. Since there are four points, and not three, it is possible to make a hole in the “triangle” by rearranging the parts to make it concave or convex. End of story.

Quick Calculate

In theory both of these websites should be very convenient. But in application, Wolfram Alpha shows how much more time has been spent on it. For example, searching for ‘cabbage’, in both engines, brings back very different results. For Google Squared, a list is brought back, filled with things grabbed seemingly at random from the web. The first result is Garlic, the second is cabbage but is mislabeled as ‘vegetable’, and so on. It is obvious from looking at it that the search is still just looking through web pages and returning (somewhat) relevant paragraphs. It should be noted that Google Squared works better at lists of things, but not as well for single entities. Searching for ‘cars’ returns a handy list of auto makers, like Chevrolet, Honda, Toyota, etc. However, past the item description and image, the other variables are rarely useful, and more than half the time return ‘no value found’.

Wolfram Alpha, on the other hand, couldn’t be more helpful. The example ‘cabbage’, brings back more information than any one person should know about it. The first information shown is a nutritional facts box, showing details about the content of cabbage. This is followed by separate tabs for daily vitamin and mineral %, its ranking compared to other foods for daily %, and more detailed information about its calories, carbs, fat, proteins, and so on. Unlike Google Squared, however, searching for something like ‘cars’ does not bring back results, because ‘cars’ is a generality. Specific things like ‘Ford’ or ‘Toyota’, or even ‘Ford, Toyota’ at once will bring back detailed stock information about the companies you list, separated by commas. Just with those two words, for any company, will return trading prices, financial info, fundamentals, stock changes over the past day to the past 5 years, performance comparisons, projections, and so on. This is just one of the many uses of Wolfram Alpha. It can also produce information about physics, chemistry, health and medicine, weather, socioeconomic data, places, words, people, media, and so much more. It can even solve almost any math problem instantly, just by entering the equation into the search.

If not obvious by now, Wolfram Alpha is clearly the superior engine. In addition to displaying information easier and more accurately, it also can handle an incredible range of queries. The one thing you should take from this article is that Wolfram Alpha is an excellent source for any data you might need to find online. The next time you have any kind of report that needs statistics, be sure to remember Wolfram.

http://www.google.com/squared

http://www.wolframalpha.com/

Quick Math

Stay tuned for more regular updates next week!

1. Keep study area clean & well lit – Nothing is worse than having to study in a dark, messy room or at a filthy desk.  Nobody wants to do it: especially you.  This is why it’s important to always try to work in a well lit, clean environment to avoid distractions.
2. Keep a positive attitude – The easiest way to be unsuccessful is to convince yourself you’re going to be unsuccessful.  On the contrary, if you keep positive and convince yourself that studying is going to help you, you’re likely to be much more confident about both the math and yourself.
3. Set realistic and attainable goals – Don’t bite off more than you can chew.  Set goals you can both measure and reach, such as committing to learning 4 new formulas or proofs a day.  Making your goal ‘to be better at math’ does not work, because you have no way to gauge if you are achieving your goal or not.
4. Take a break once an hour – It is important not to get too overwhelmed, especially when studying math.  For every hour spent studying, take a ten or fifteen minute break, to give yourself some time to digest the important points before getting back to work.
5. Summarize most important points – By really figuring out what parts are most important, and writing them down, it helps you to remember what they are.  Try reading all of the main points out loud to yourself or to someone else; the more senses you use to help you remember, the better.
6. Study at the same time every day – Once you get into the habit of studying at say, 4:30 every day, your brain becomes familiar with the time and it will be easier and easier to focus on your work, and will take less time to get into a math state of mind.
7. Practice, practice, practice, the tough questions – This last one is a no brainer.  If you’re having trouble with a certain formula, or equation that just isn’t working the way it should, the solution is to keep practicing with it and similar equations until it begins to make sense.  Like the saying goes, ‘Practice makes perfect.’