Handy everyday number formulas people use?

genuine leather

Firstly im no maths genius, pretty basic, but i manage and enjoy reasoning(only:) )
the sheer possibilities of maths. I do roofing so pythagoras is my friend.

Just wondering what simple formulas people might use in their daily rounds.

Simple Eg, 25 x any number(add two zeros divide by four)

25x36
3600/4
900

yeah simple i know:)

Gwynston

As my son is going through the laborious process of learning his times tables, I've discovered that my wife and I, in helping him have little (diferent) formulae we use to help us do mental arithmetic.

I kind of never noticed, and upon reflection some seem kind of silly or simple, but finding out my wife does similar things in different ways suggests to me that most people probably do the same kinds of things.

Examples:
1) The 9 times table - it's easier to me to just use the 10x table and subtract one of the numbers being multiplied. e.g. 9 times 8 is 80 minus 8 = 72.
(Also: 11x table, but add one)

2) The 5 times table is similar. Use the 10x table and chop in half!

3) When adding numbers, I subconsciously think to the nearest 10. I instinctively know the number pairs that make ten: 1+9, 2+8, 3+7, 4+6 etc. and everything else is relative to those. e.g. 17 + 24 I know the unit column will be a 1 because the number pair 7+4 is 1 more than 7+3!

My wife's an accountant and her mental arithmetic is actually pretty shabby. I think she relies on calculators and Excel too much!

Particularly division - I find I can to approximate mental division pretty well (like dividing a restaurant bill). It would take me a while to get the perfect answer, but somehow I'm able to reach a rough answer almost instantly and be accurate enough - withing a couple of percent.

Tweej

9 times tables, done easy

Stick out your hand, with all 8 fingers and 2 thumbs extended

Multiplying 9 by 4? Lower your 4th finger from the left

Now count the number of fingers on the left and on the right

3,6

36

kboc

search for "digital roots" on internet.

especially see here and here

Some lovely connections betwen numbers which help you with mult and division

Good luck

genuine leather

Tweej wrote: »

9 times tables, done easy

Stick out your hand, with all 8 fingers and 2 thumbs extended

Multiplying 9 by 4? Lower your 4th finger from the left

Now count the number of fingers on the left and on the right

3,6

36

So it would prob take you awhile to explain the theory of relativity on your fingers yeah......i ll put on the kettle

bnt

I'm fascinated by how the decimal versions of 7ths (1/7, 2/7 ... 6/7) all consist of the same looping 6-digit sequence of numbers (142857), the only difference being the start point in the loop:

• for 1/7, start on 14: 0.142857142857...
• for 2/7, start on 28: 0.285714285714...
• for 3/7, start on 42: 0.428571428571...
• for 4/7, start on 55: 0.571428571428...
• for 5/7, start on 71: 0.714285714285...
• for 6/7, start on 85: 0.857142857142...

Yakuza

bnt wrote: »

I'm fascinated by how the decimal versions of 7ths (1/7, 2/7 ... 6/7) all consist of the same looping 6-digit sequence of numbers (142857), the only difference being the start point in the loop:

• for 1/7, start on 14: 0.142857142857...
• for 2/7, start on 28: 0.285714285714...
• for 3/7, start on 42: 0.428571428571...
• for 4/7, start on 55: 0.571428571428...
• for 5/7, start on 71: 0.714285714285...
• for 5/7, start on 85: 0.857142857142...

That's an example of a cyclic number. The reciprocal of a prime p repeats after p-1 digits (other than 2 or 5).

Some tricks I use (and have shown my eldest child (11)):
Squaring a number (call it x) - pick a number (y) that brings x to nearest multiple of 10 (y can be from -5 to +5). Multiply (x+y) by (x-y) and add y². This will give you x².
(This is because (x-y)(x+y) + y² = [x² - y²] + y² = x²)

e.g. 63² = 60 * 66 + 3² = 3960+9 = 3969

An even shorter trick for squaring a multiple of 5 : take the number shown by digits to the left of the 5, multiply it by itself plus 1, write that down and append 25.
eg: 25² = write down the product of 2*3 and then 25 = 625.
or 75² = write down the product of 7*8 and then 25 = 5625.

Adding the first n numbers (1+2+3+...+(n-1)+n) = n(n+1)/2.

Similar to the OP, multplying by 5 is easier done by adding a zero and dividing by 2