Maths Trick

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<p>1. The 11 Times Trick We all know the trick when multiplying by ten add 0 to the end of the number, but did you know there is an equally easy trick for multiplying a two digit number by 11? This is it: Take the original number and imagine a space between the two digits (in this example we will use 52: 5_2 Now add the two numbers together and put them in the middle: 5_(5+2)_2 That is it you have the answer: 572. If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first: 9_(9+9)_9 (9+1)_8_9 10_8_9 1089 It works every time. 2. Quick Square If you need to square a 2 digit number ending in 5, you can do so very easily with this trick. Mulitply the first digit by itself + 1, and put 25 on the end. That is all! 252 = (2x(2+1)) &amp; 25 2x3=6 625 3. Multiply by 5 Most people memorize the 5 times tables very easily, but when you get in to larger numbers it gets more complex or does it? This trick is super easy. Take any number, then divide it by 2 (in other words, halve the number). If the result is whole, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end. It works everytime:</p> <p>2682 x 5 = (2682 / 2) &amp; 5 or 0 2682 / 2 = 1341 (whole number so add 0) 13410 Lets try another: 5887 x 5 2943.5 (fractional number (ignore remainder, add 5) 29435</p> <p>4. Multiply by 9 This one is simple to multiple any number between 1 and 9 by 9 hold both hands in front of your face drop the finger that corresponds to the number you are multiplying (for example 93 drop your third finger) count the fingers before the dropped finger (in the case of 93 it is 2) then count the numbers after (in this case 7) the answer is 27. 5. Multiply by 4 This is a very simple trick which may appear obvious to some, but to others it is not. The trick is to simply multiply by two, then multiply by two again: 58 x 4 = (58 x 2) + (58 x 2) = (116) + (116) = 232</p> <p>6. Calculate a Tip If you need to leave a 15% tip, here is the easy way to do it. Work out 10% (divide the number by 10) then add that number to half its value and you have your answer: 15% of $25 = (10% of 25) + ((10% of 25) / 2) $2.50 + $1.25 = $3.75 7. Tough Multiplication If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer: 32 x 125, is the same as: 16 x 250 is the same as: 8 x 500 is the same as: 4 x 1000 = 4,000</p> <p>8. Dividing by 5 Dividing a large number by five is actually very simple. All you do is multiply by 2 and move the decimal point: 195 / 5 Step1: 195 * 2 = 390 Step2: Move the decimal: 39.0 or just 39 2978 / 5 step 1: 2978 * 2 = 5956 Step2: 595.6</p> <p>9. Subtracting from 1,000 To subtract a large number from 1,000 you can use this basic rule: subtract all but the last number from 9, then subtract the last number from 10: 1000 -648 step1: subtract 6 from 9 = 3 step2: subtract 4 from 9 = 5 step3: subtract 8 from 10 = 2 answer: 352 10. Assorted Multiplication Rules Multiply by 5: Multiply by 10 and divide by 2. Multiply by 6: Sometimes multiplying by 3 and then 2 is easy. Multiply by 9: Multiply by 10 and subtract the original number. Multiply by 12: Multiply by 10 and add twice the original number. Multiply by 13: Multiply by 3 and add 10 times original number. Multiply by 14: Multiply by 7 and then multiply by 2 Multiply by 15: Multiply by 10 and add 5 times the original number, as above. Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2. Multiply by 17: Multiply by 7 and add 10 times original number. Multiply by 18: Multiply by 20 and subtract twice the original number (which is obvious from the first step). Multiply by 19: Multiply by 20 and subtract the original number. Multiply by 24: Multiply by 8 and then multiply by 3. Multiply by 27: Multiply by 30 and subtract 3 times the original number (which is obvious from the first step). Multiply by 45: Multiply by 50 and subtract 5 times the original number (which is obvious from the first step). Multiply by 90: Multiply by 9 (as above) and put a zero on the right. Multiply by 98: Multiply by 100 and subtract twice the original number. Multiply by 99: Multiply by 100 and subtract the original number. Bonus: Percentages Yanni in comment 23 gave an excellent tip for working out percentages, so I have taken the liberty of duplicating it here: Find 7 % of 300. Sound Difficult?</p> <p>Percents: First of all you need to understand the word Percent. The first part is PER , as in 10 tricks per listverse page. PER = FOR EACH. The second part of the word is CENT, as in 100. Like Century = 100 years. 100 CENTS in 1 dollar etc. Ok so PERCENT = For Each 100. So, it follows that 7 PERCENT of 100, is 7. (7 for each hundred, of only 1 hundred). 8 % of 100 = 8. 35.73% of 100 = 35.73 But how is that useful?? Back to the 7% of 300 question. 7% of the first hundred is 7. 7% of 2nd hundred is also 7, and yep, 7% of the 3rd hundred is also 7. So 7+7+7 = 21. If 8 % of 100 is 8, it follows that 8% of 50 is half of 8 , or 4. Break down every number thats asked into questions of 100, if the number is less then 100, then move the decimal point accordingly. EXAMPLES: 8%200 = ? 8 + 8 = 16. 8%250 = ? 8 + 8 + 4 = 20. 8%25 = 2.0 (Moving the decimal back). 15%300 = 15+15+15 =45. 15%350 = 15+15+15+7.5 = 52.5 Also its usefull to know that you can always flip percents, like 3% of 100 is the same as 100% of 3. 35% of 8 is the same as 8% of 35.</p> <p>http://www.glad2teach.co.uk/fast_maths_calculation_tricks.htm</p> <p>3.</p> <p>Wild About Math!Making Math fun and accessible </p> <p>Home About Articles Math contest problem links Videos</p> <p>Impress your friends with mental Math tricksNovember 11th, 2007 | by Sol |</p> <p>See Math tricks on video at the Wild About Math! mathcasts page.</p> <p>_____________________ Being able to perform arithmetic quickly and mentally can greatly boost your self-esteem, especially if you dont consider yourself to be very good at Math. And, getting comfortable with arithmetic might just motivate you to dive deeper into other things mathematical. This article presents nine ideas that will hopefully get you to look at arithmetic as a game, one in which you can see patterns among numbers and pick then apply the right trick to quickly doing the calculation. The tricks in this article all involve multiplication. Dont be discouraged if the tricks seem difficult at first. Learn one trick at a time. Read the description, explanation, and examples several times for each technique youre learning. Then make up some of your own examples and practice the technique. As you learn and practice the tricks make sure you check your results by doing multiplication the way youre used to, until the tricks start to become second nature. Checking your results is critically important: the last thing you want to do is learn the tricks incorrectly. 1. Multiplying by 9, or 99, or 999 Multiplying by 9 is really multiplying by 10-1. So, 99 is just 9x(10-1) which is 910-9 which is 90-9 or 81. Lets try a harder example: 469 = 4610-46 = 460-46 = 414. One more example: 689 = 680-68 = 612. To multiply by 99, you multiply by 100-1. So, 4699 = 46x(100-1) = 4600-46 = 4554. Multiplying by 999 is similar to multiplying by 9 and by 99. 38999 = 38x(1000-1) = 38000-38 = 37962. 2. Multiplying by 11</p> <p>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, 43611 = is 4796. Lets do another example: 325411. 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: 465711. 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, 465711 = 51227 . 3. Multiplying by 5, 25, or 125</p> <p>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. 125 = (1210)/2 = 120/2 = 60. Another example: 645 = 640/2 = 320. And, 42865 = 42860/2 = 21430. To multiply by 25 you multiply by 100 (just add two 0s to the end of the number) then divide by 4, since 100 = 254. Note: to divide by 4 your can just divide by 2 twice, since 22 = 4. 6425 = 6400/4 = 3200/2 = 1600. 5825 = 5800/4 = 2900/2 = 1450. To multiply by 125, you multipy by 1000 then divide by 8 since 8125 = 1000. Notice that 8 = 22x2. So, to divide by 1000 add three 0s to the number and divide by 2 three times. 32125 = 32000/8 = 16000/4 = 8000/2 = 4000. 48125 = 48000/8 = 24000/4 = 12000/2 = 6000. 4. Multiplying together two numbers that differ by a small even number This trick only works if youve memorized or can quickly calculate the squares of numbers. If youre able to memorize some squares and use the tricks described later for some kinds of numbers youll be able to quickly multiply together many pairs of numbers that differ by 2, or 4, or 6. Lets say you want to calculate 1214. When two numbers differ by two their product is always the square of the number in between them minus 1. 1214 = (1313)-1 = 168. 1618 = (1717)-1 = 288. 99101 = (100100)-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. 1115 = (1313)-4 = 169-4 = 165.</p> <p>1317 = (1515)-4 = 225-4 = 221. If the two numbers differ by 6 then their product is the square of their average minus 9. 1218 = (1515)-9 = 216. 1723 = (2020)-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. 3535 ends in 25. We get the rest of the product by multiplying 3 by one more than 3. So, 34 = 12 and thats the rest of the product. Thus, 3535 = 1225. To calculate 6565, notice that 67 = 42 and write down 4225 as the answer. 8585: Calculate 89 = 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 Lets 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 4248: Multiply 4 by 4+1. So, 45 = 20. Write down 20. Multiply together the last digits: 28 = 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: 6466. 67 = 42. 46 = 24. The product is 4224. A final example: 8684. 89 = 72. 64 = 24. The product is 7224 7. Squaring other 2-digit numbers</p> <p>Lets say you want to square 58. Square each digit and write a partial answer. 55 = 25. 88 = 64. Write down 2564 to start. Then, multiply the two digits of the number youre squaring together, 58=40. Double this product: 402=80, then add a 0 to it, getting 800. Add 800 to 2564 to get 3364. This is pretty complicated so lets do more examples. 3232. The first part of the answer comes from squaring 3 and 2. 33=9. 22 = 4. Write down 0904. Notice the extra zeros. Its important that every square in the partial product have two digits. Multiply the digits, 2 and 3, together and double the whole thing. 23x2 = 12. Add a zero to get 120. Add 120 to the partial product, 0904, and we get 1024. 5656. The partial product comes from 55 and 66. Write down 2536. 56x2 = 60. Add a zero to get 600. 5656 = 2536+600 = 3136. One more example: 6767. Write down 3649 as the partial product. 67x2 = 422 = 84. Add a zero to get 840. 6767=3649+840 = 4489. 8. Multiplying by doubling and halving There are cases when youre 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. Lets say you want to multiply 14 by 16. You can do this: 1416 = 288 = 564 = 1122 = 224. Another example: 1215 = 630 = 63 with a 0 at the end so its 180. 4817 = 2434 = 1268 = 6136 = 3272 = 816. (Being able to calculate that 327 = 81 in your head is very helpful for this problem.)</p> <p>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 = 22x22. 1516: 152 = 30. 302 = 60. 602 = 120. 1202 = 240. 238: 232 = 46. 462 = 92. 922 = 184. 548: 542 = 108. 1082 = 216. 2162 = 432. Practice these tricks and youll get good at solving many different kinds of arithmetic problems in your head, or at least quickly on paper. Half the fun is identifying which trick to use. Sometimes more than one trick will apply and youll get to choose which one is easiest for a particular problem. Multiplication can be a great sport! Enjoy. See Math tricks on video at the Wild About Math! mathcasts page. Check out these related articles: </p> <p>Quick multiplication by 12: A gentle introduction to Trachtenberg speed mathematics Help kids learn multiplication with this visual approach How to square large numbers quickly (part 1) How to get past stupid Math mistakes</p> <p>ShareThis</p> <p>If you enjoyed this post, make sure you subscribe to my RSS feed!</p> <p>1. 222 Responses to Impress your friends with mental Math tricks2. By Alex Kay on Nov 19, 2007 | Reply Hey there! Just wanted to stop by and say thanks for a great post and read - math doesnt have to be boring! Have a nice day, Alex 3. By Sol on Nov 19, 2007 | Reply Alex,</p> <p>Youre quite welcome. Glad you liked it. Sol 4. By Karen (Karooch from Scraps of Mind) on Nov 19, 2007 | Reply Hey Sol i dont expect to be using them to impress anybody, but some of those techniques will come in very handy. Thanks a lot. Ill give it a Stumble so others can learn them too. 5. By Sol on Nov 19, 2007 | Reply Karen, Thanks for the kind words and the stumbling. Sol 6. By DJ in Houston on Nov 19, 2007 | Reply WOW!!! I wish I knew this while I was in school!!! That is neat 7. By Alan on Nov 21, 2007 | Reply Very cool - I plan to use this as often as possible. By the way there is a minor typo So, 4699 = 4600x(100-1) = 4600-46 = 4554. should read So, 4699 = 46x(100-1) = 4600-46 = 4554. thats ok though - this page...</p>