Many things I was made to learn at school I have never had to use. Over the years, however, I have had occasions to use trigonometry, geometry and arithmetic. Maths was not one of my best subjects at school! With time I have got more dexterous with numbers but do not regard it as a strong suit. This is relative, of course. To the astonishment of younger generations I have been known to multiply numbers together without using my phone!
Over the last week I have been reading “Mind Performance Hacks” by Ron Hale-Evans. A very interesting book with many varied ideas. To my surprise I found the maths section far more engaging than I expected. This lead me to a book called “Rapid Math Tricks and Tips” by Edward H. Julius. I never thought I would enjoy reading a mathematics book, but I did! This book is a fast and easy read and is full of techniques that will improve your handling of numbers. The book says “thirty days” but I read most of it in an afternoon and intend to reread it today.
I have come to the revelation that arithmetic is rather like judo. You learn a few basic principles and then you may wrestle the numbers into submission.
Some insights and observations:
z x y = 2z x ½y = 3z x ⅓y = nz x y/n
which is my way of remembering that when multiplying you can change one number if you chance the other by the same quantity. For example, if you halve the multiplicand you must double the multiplier or vice versa. In other words:
66 x 3.5 = 33 x 7, but one may be much easier for you to calculate.
Similarly, with division:
z/y = 2z/2y = 3z/3y = nz/ny
This is easy to remember if recall a division is essentially a fraction, and top and bottom must balance. You must change dividend and divisor by the same proportion. Hence:
34 ÷ 4.5 = 68 ÷ 9
Breaking numbers up is another useful trick:
For example:
47 x 14
can be reorganized as
(50 – 3) x 7 x 2 or (40 + 7) x 7 x 2
Since I find threes and fives easier than my seven-times table I would solve this as:
7(50-3) x 2 = (350 – 21) x 2 = 329 x 2 = 685
When you split a number keep track of if you have to subtract or add the elements.
Solving the above I used another useful trick, which is subtracting by addition. What do I need to add to “21” to make it “350” ? If I add a “9” it becomes “30”. 30 needs “320” to become “350”. Therefore the difference is “9 + 350”. The book suggests doing the “tens” first: 21 needs 320 to make 341, then 9. OR, you can reorganize: 350 - 21 = 350 - 20 - 1.
When I was at school I was taught you divided numbers from the left hand side, but multiplication, addition and subtraction was to be done from the right.
THEY LIED!
This book has lots of examples where addition or multiplication are simpler if you start on the left. One of my favourites is the method where you run down one column, up the next, down the one after that and so forth.
The book has many other useful techniques. Many are quite simple but may not have occurred to you if you are uncomfortable with numbers. For example, rather than multiplying by “8” you may find it easier to double a number, double the result and double again. To divide by 16, quarter the number and quarter the result. Dividing by 3 and then 2 may be easier than attempting to divide by 6. One way to quickly multiply by 9 is to add a zero to the number and then subtract the original number from this. This is treating x9 as x(10 - 1).
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The Books
The Books