Math can be terrifying for many people. This list will hopefully improve your general knowledge of mathematical tricks and your speed when you need to do math in your head.

So here's 9 super mental math tricks...

 

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. One more example: 68×9 = 680-68 = 612. To multiply by 99, you multiply by 100-1. So, 46×99 = 46x(100-1) = 4600-46 = 4554. Multiplying by 999 is similar to multiplying by 9 and by 99. 38×999 = 38x(1000-1) = 38000-38 = 37962.

 

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. Let’s do another example: 3254×11. The answer comes from these sums and edge numbers: (3)(3+2)(2+5)(5+4)(4) = 35794. One more example, this one involving carrying: 4657×11. Write down the sums and edge numbers: (4)(4+6)(6+5)(5+7)(7). Going from right to left we write down 7. Then we notice that 5+7=12. So we write down 2 and carry the 1. 6+5 = 11, plus the 1 we carried = 12. So, we write down the 2 and carry the 1. 4+6 = 10, plus the 1 we carried = 11. So, we write down the 1 and carry the 1. To the leftmost digit, 4, we add the 1 we carried. So, 4657×11 = 51227 .

 

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, since 100 = 25×4. Note: to divide by 4 your can just divide by 2 twice, since 2×2 = 4. 64×25 = 6400/4 = 3200/2 = 1600. 58×25 = 5800/4 = 2900/2 = 1450. To multiply by 125, you multipy by 1000 then divide by 8 since 8×125 = 1000. Notice that 8 = 2×2x2. So, to divide by 1000 add three 0’s to the number and divide by 2 three times. 32×125 = 32000/8 = 16000/4 = 8000/2 = 4000. 48×125 = 48000/8 = 24000/4 = 12000/2 = 6000.

 

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. 99×101 = (100×100)-1 = 10000-1 = 9999 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. 12×18 = (15×15)-9 = 216. 17×23 = (20×20)-9 = 391.

 

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. To calculate 65×65, notice that 6×7 = 42 and write down 4225 as the answer. 85×85: Calculate 8×9 = 72 and write down 7225.

 

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. Notice that for this particular example you could also have noticed that 42 and 48 differ by 6 and have applied technique number 4. Another example: 64×66. 6×7 = 42. 4×6 = 24. The product is 4224. A final example: 86×84. 8×9 = 72. 6×4 = 24. The product is 7224

 

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. This is pretty complicated so let’s do more examples. 32×32. The first part of the answer comes from squaring 3 and 2. 3×3=9. 2×2 = 4. Write down 0904. Notice the extra zeros. It’s important that every square in the partial product have two digits. Multiply the digits, 2 and 3, together and double the whole thing. 2×3x2 = 12. Add a zero to get 120. Add 120 to the partial product, 0904, and we get 1024. 56×56. The partial product comes from 5×5 and 6×6. Write down 2536. 5×6x2 = 60. Add a zero to get 600. 56×56 = 2536+600 = 3136. One more example: 67×67. Write down 3649 as the partial product. 6×7x2 = 42×2 = 84. Add a zero to get 840. 67×67=3649+840 = 4489.

 

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. Another example: 12×15 = 6×30 = 6×3 with a 0 at the end so it’s 180. 48×17 = 24×34 = 12×68 = 6×136 = 3×272 = 816. (Being able to calculate that 3×27 = 81 in your head is very helpful for this problem.)

 

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. 23×8: 23×2 = 46. 46×2 = 92. 92×2 = 184. 54×8: 54×2 = 108. 108×2 = 216. 216×2 = 432.

See related article: Beauty of Mathematics


Article Info & Options:
Date: 29 Oct 2008 | Author: mesmerX | Category: News | Views: 94758

» TrackBack
» Print
» RSS

Enojyed this article? Share it and let others know:
Share/Bookmark



Comments: 29

Guest
smile laughing angry crying

tom
I love math smile

Guest
laughing sad angry crying smile wink wassat tongue sad angry crying

Guest
I really do not get it

Photius
More ArithmeTricks :

arscalcula.com/archives.shtml

Niki
Miss.CaponigroI think when you put the homework quiezs on the Communique is a very smart idea why I think that is because say we loose it we can go on and go on the math home page and just print it out and maybe if we have any questions about the homework quiezs we can go on the math home page and just ask you a question if we are stuck and the last reason is say one of the give me 5 people are absent and they are supposed to show you there 5 promblems but they are not in school so they post there answer on the math home page and you can tell them if they are right or wrong.That is why I think you putting the homework quiezs on the Communique is a very smart idea.Joli

Guest
To the user that said, "It takes less mental effort to use pencil and paper."

No kidding. I think my IQ went down 10 points reading that comment.

Here's another trick to use when multiplying 9 by any single digit number :

- Subtract 1 from the number that's being multiplied by 9, then add the number that will make the sum of the two numbers = 9.

9 *8 = (8-1) = 7, then 7+2 =9. Answer = 72

Guest
Please make a graph. Multiplication tables would be a lot easier to understand. Sometimes things are more difficult merely because they were portrayed wrong.

PINKY
crying sad laughing smile wink wassat

Guest
The world needs garbagemen so do not despair if you are stumped. It's okay. Your mother probably still loves you.

Guest
smile

gest
did not understand a word angry

Guest
angry
i hate math

Guest
Your probably never going to get a problem that follows every rule needed for these specific tricks.

Guest
Dave your trick is wonderful, i am really impress by your work

Guest
@Guest: A course I took in high school, precalc, forbade the use of calculators and kind of looked down on pencil and paper without strictly ruling out its use. Aside from the first time I would learn a certain mathematical principle, lesson, or idea in the class I never used pencil and paper. The idea is that if you can learn to do these things first without calculators and then completely in your head, it leaves you able to do more complicated parts of the problem out in those methods while saving the "easy" stuff for mental math. Do you pull out pencil and paper for problems like 2 + 4? You did when you were very young. Now you know the answer automatically from having done the math so many times mentally. Doing problems in your head is not as precise but, with practice, sharpens the mind and allows for further learning.

Guest
smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile

Guest
smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile wink wassat tongue laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing laughing smile smile smile smile smile smile smile smile smile smile smile

Guest
smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile smile wink wassat wassat wassat wassat wassat wassat wassat wassat wassat wassat tongue tongue tongue tongue tongue laughing laughing laughing laughing sad sad sad angry angry angry angry angry crying angry crying

josh
smile wink wassat tongue laughing sad angry crying

Guest
i use a lot of these tricks. try multiplying by averages.

42 * 57
40 * 60 = 2400
now add two more 60s
42 * 60 = 2520
now take away three 42s (which is 126)
42 * 57 = 2394

this works on any numbers of any size

Guest
GAY!!!

Guest
smile wink wassat tongue laughing sad angry crying

Guest
multication wow smile

Guest
I always do num. 8. ^_^

Guest
it takes less effort to write it all down and less mental effort. being prepared for your day would be a better idea. to further distil this... if you know you will have to do this kind of math, try showing up with a pencil, a piece of paper, and a calculator. then write down the numbers and then do the math. why would anyone who needed to remember all of these numbers want to risk forgetting any one number and risk getting the wrong answer and thereby wasting everyones' time.

saily
smile wink wassat tongue laughing angry wassat laughing crying sad laughing

Dave
Following trick #1
multiply by 8: 45(10-2)=360, 8(10-2)=(8*10)-(8-2)=64
multiply by 7: 7(10-3)=70-21=49

etc.

dash gobe
impressive

comments powered by Disqus


Copyright Message

© 2015 DailyCognition.com