Everyone gets really wow’d when someone pulls of some execptional mental maths.
The best part is, you can totally be that guy at the party with a little practice and preparation.
What follows is 10 maths tricks you can memorize, practice or internalize so you can whip them out anywhere to dazzle those around you, whether it’s the trading floor or a cocktail party.
Eric Platt contributed to an earlier version of this report.
Squaring large numbers can be a real pain sometimes. But if you're plugging something into a formula, easy mental squaring could be a huge asset.
So say you've got a number, x, that you want to square.
Find 'd' the difference between the nearest multiple of 10 and x.
Then, multiply (x-d) and (x+d). This should be much easier, because one of the numbers is a multiple of 10. Just add d2, and you've got your square.
Here's an example. I want to find the square of 84. The nearest multiple of 10 is 80, so d is 4.
x+d is 88, x-d is 80.
88 X 80 = 6400 + 640 = 7040. Add 42 = 16, and you get 7056.
That process, once you get the hang of it, is much easier than just attacking 842 head on.
This description comes from commenter Imwangi:
A nice trick I've been using to find square roots follows. It assumes that you know a couple of common squares and their roots. For example, 7-> 49, 11 -> 121, 13 ->169...
Let's take a number 86.
1) Get the closest square == 81
2) Divide 86 by the square root of the closest square = 9 and 5/9 == 9.555
3) Average the figure from (2) above and the square: (9 + 9.555)/2 == 9.277 Note that this is effectively halving the remainder from step 2 == 9+ 2.5/9
4) You have a pretty good estimate! 9.273 is the real answer.
Picking squares that are closer to the number improves accuracy
Who hasn't kvetched (or bragged) about their salary at a party? It's even more fun when you can break it down to an hourly rate.
You're a salaried employee and trying to figure out how much that wage earns you an hour, maybe for that part-time job you're considering taking on. Take your salary, drop the last three zeros and then divide by the number two.
So if you earn $40,000, you're left with $20 an hour. Numbers work best if you're only working a 40 hour week.
This one is a great party trick, provided you find yourself at a terrible party where other guests are discussing repeating decimals.
Repeating decimals are a pain, and oftentimes basic calculators have trouble getting down to brass tacks by rephrasing them as a fraction.
All you need to do to turn a repeating decimal (0.636363...) into a lovely fraction is:
- Find the number that repeats (63)
- Figure out how many places that number has (2)
- Divide the repeater by a number with the same number of places made up of nines (in this case, 99)
So we know 0.636363... = 63/99 = 7/11.
You can do this with much larger repeating numbers as well. 0.726726... is equal to 726/999 which reduces to 242/333.
This one comes from commenter David Fogden:
You take a number like 35. You ignore the final 5, multiply what is left by itself+1, then insert 25 at the end as a suffix.
Here's an example:
Square of 35: 3 x (3+1) = 12 and add 25 as the suffix = 1225
Square of 105: 10 x (10+1) = 110, add the suffix = 11025
Dividing by 7 is probably the most annoying possible aspect of simple arithmetic. There are relatively simple strategies and mental tricks for all of the other divisors between 1 and 10, by 7 stands alone.
Here's where division comes in. Lets say you wanted to divide 9573 by 7. Let's work from the left.
Start with thousands. So 9/7 = 1 with a remainder of 2. So our first digit is 1.
Since we had a remainder of 2, and the hundreds digit is 5, we next get 25/7 = 3 with a remainder of 4. So our next digit is 3.
We have a remainder of 4, and the tens place we have a 7, so we have 47/7 = 6 with a remainder of 5.
We have a remainder of 5, and in the ones place we have a 3. So 53/7 = 7, with a remainder of 4.
We remember, then that 4/7 is equal to .571428 repeating.
So 9573 divided by 7 is 1367.571428 repeating.
You can use factorials to remember easy stats about time.
- There are 4! (or 4*3*2*1) hours in a day.
- There are 8! minutes in 4 weeks
- There are 10! seconds in 6 weeks.
The basic rule for multiplying by 11 is this:
10y + y. So 33 x 11 = 330 + 33.
However, you might need something a little more powerful...
When multiplying a figure by the number 11, follow this pattern: leave the last and first digits alone, then sum each and every pair of digits next to each other (this makes most sense when seen in example):
1. 4,281 x 11 becomes the following digits: (4)(4+2),(2+8)(8+1)(1) or 47,091
When the sum of a pair is greater than 10, carry that digit to the next left pair (as seen above, where 2+8 was 10)
2. Let's try something harder. 9,621,576,521 x 11 becomes: (9)(9+6),(6+2)(2+1)(1+5),(5+7)(7+6)(6+5),(5+2)(2+1)(1) or 105,837,341,731
Converting fractions to decimals are usually pretty easy when the number in the denominator is less than 10. The glaring exception is with 7 in the denominator.
The one thing you need to remember in order to divide by 7 is that 1/7 = .142857 repeating. That's the key. If you can remember that, with a little practice, dividing by 7 becomes a breeze.
The next thing that you have to realise is that multiples of that just cycle through the six numbers. For example, 2/7 = .285714 repeating. Notice what just happened?
The numbers always cycle in the same sequence. For 1/7, the cycle starts at 1, the lowest digit. For 2/7, the cycle starts with 2, the second lowest digit. For 3/7, (.428571 repeating) the cycle starts with the 4, the third lowest digit. That's the process.
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