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Aug 19

Mental Math Tricks

Posted by abiao at 10:26 | Others | Comments(0) | Reads(9562)
I remember vividly when I was at my elementary school, an author of a book about mental Math tricks stood in front of all of us, challenged everyone by calculating mentally 2-digit multiplication in few seconds. That was really amazing for young kids, even now mental math multiplication is still a game when having beer with my friends, "um... so what is 15*17?", 1, 2, 3, no answer? DRINK! A lot of fun indeed.

Stumbled a site just now about 9 mental math tricks, (I assume many of us head of Stumbleupon, if not, in one sentence: StumbleUpon helps you discover and share great websites matched to your personal preferences with your friends, for instance, you can follow & see my stumbles at https://www.stumbleupon.com/stumbler/biao/.) it is a good one explaining the tricks in very detail, I am sure you will be able to compute many 2-digit multiplication in 5 seconds mentally. Be preapred to show off in a dinner.

1. Multiplying by 9, or 99, or 999
Multiplying by 9 is really multiplying by 10-1. So, 9×9 is just 9x(10-1) which is 9×10-9 which is 90-9 or 81. Let’s try a harder example: 46×9 = 46×10-46 = 460-46 = 414.

2. Multiplying by 11
To multiply a number by 11 you add pairs of numbers next to each other, except for the numbers on the edges. Let me illustrate: To multiply 436 by 11 go from right to left. First write down the 6 then add 6 to its neighbor on the left, 3, to get 9. Write down 9 to the left of 6. Then add 4 to 3 to get 7. Write down 7. Then, write down the leftmost digit, 4. So, 436×11 = is 4796.

3. Multiplying by 5, 25, or 125
Multiplying by 5 is just multiplying by 10 and then dividing by 2. Note: To multiply by 10 just add a 0 to the end of the number.
12×5 = (12×10)/2 = 120/2 = 60. Another example: 64×5 = 640/2 = 320. And, 4286×5 = 42860/2 = 21430. To multiply by 25 you multiply by 100 (just add two 0’s to the end of the number) then divide by 4. To multiply by 125, you multipy by 1000 then divide by 8 since 8×125 = 1000.

4. Multiplying together two numbers that differ by a small even number
This trick only works if you’ve memorized or can quickly calculate the squares of numbers. If you’re able to memorize some squares and use the tricks described later for some kinds of numbers you’ll be able to quickly multiply together many pairs of numbers that differ by 2, or 4, or 6. Let’s say you want to calculate 12×14. When two numbers differ by two their product is always the square of the number in between them minus 1.
12×14 = (13×13)-1 = 168.
16×18 = (17×17)-1 = 288.
If two numbers differ by 4 then their product is the square of the number in the middle (the average of the two numbers) minus 4.
11×15 = (13×13)-4 = 169-4 = 165.
13×17 = (15×15)-4 = 225-4 = 221.
If the two numbers differ by 6 then their product is the square of their average minus 9.

5. Squaring 2-digit numbers that end in 5
If a number ends in 5 then its square always ends in 25. To get the rest of the product take the left digit and multiply it by one more than itself. 35×35 ends in 25. We get the rest of the product by multiplying 3 by one more than 3. So, 3×4 = 12 and that’s the rest of the product. Thus, 35×35 = 1225.

6. Multiplying together 2-digit numbers where the first digits are the same and the last digits sum to 10
Let’s say you want to multiply 42 by 48. You notice that the first digit is 4 in both cases. You also notice that the other digits, 2 and 8, sum to 10. You can then use this trick: multiply the first digit by one more than itself to get the first part of the answer and multiply the last digits together to get the second (right) part of the answer.An illustration is in order:
To calculate 42×48: Multiply 4 by 4+1. So, 4×5 = 20. Write down 20. Multiply together the last digits: 2×8 = 16. Write down 16. The product of 42 and 48 is thus 2016.

7. Squaring other 2-digit numbers
Let’s say you want to square 58. Square each digit and write a partial answer. 5×5 = 25. 8×8 = 64. Write down 2564 to start. Then, multiply the two digits of the number you’re squaring together, 5×8=40. Double this product: 40×2=80, then add a 0 to it, getting 800. Add 800 to 2564 to get 3364.

8. Multiplying by doubling and halving
There are cases when you’re multiplying two numbers together and one of the numbers is even. In this case you can divide that number by two and multiply the other number by 2. You can do this over and over until you get to multiplication this is easy for you to do. Let’s say you want to multiply 14 by 16. You can do this:
14×16 = 28×8 = 56×4 = 112×2 = 224.

9. Multiplying by a power of 2
To multiply a number by 2, 4, 8, 16, 32, or some other power of 2 just keep doubling the product as many times as necessary. If you want to multiply by 16 then double the number 4 times since 16 = 2×2x2×2.
15×16: 15×2 = 30. 30×2 = 60. 60×2 = 120. 120×2 = 240.

That's enough for today, I am sure there are other mental math tricks, so don't forget to share with us. For more example please read the original page at http://www.dailycognition.com/index.php/2008/10/28/9-mental-math-tricks.html, or you can buy an ebook Math Without A Calculator!


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