MATHEMATICAL SHORTCUTS

Handy shortcuts for checking calculations, without the need of a calculator!

To check addition is correct -

• add up the single digits of each individual number in the sum, until you are left with a single digit. 
  
• add these single digits together until you are, once again, left with a single digit.
  
• do the same with the total
  
• these figures should be the same

To check subtraction is correct:-

• add together the total and the number you subtracted and this should equal the number you started with.

To check multiplication is correct:-

• divide the answer by one of the numbers being multiplied.

To check division is correct:-

• multiply the answer by the number you originally divided by and this answer should be the same as the original number being divided.

HANDY HINTS

If two columns of figures should balance but don't, subtract one total from the other and if the difference is 1, 10, 100, 9 or 99 you have probably made an error in addition.

If the difference is divisible by 9 you have probably transposed a figure (e.g.  written 89 instead of 98).

This was also sent in by KB who gave the following illustration -

If your balance says 45.25 but your statement says 42.55 - the difference is 2.70 which is divisible by 9 so, therefore, it is probably a transposed figure.  You can see the 5 and 2 have been transposed.

To "square" a number (i.e. multiply a number by itself e.g. 17 x 17)

Example A - 17 x 17

Example B - 52 x 52

This shortcut was sent in by Sue Knight - thanks.

An easy way to remember your nine times table is -

a:  The figures in the answer always total 9             

e.g.        2 x 9 = 18 (1+8 = 9):
              7 x 9 = 63 (6+3 = 9)

b:  Deduct 1 from the number you are multiplying and the second number in the answer then becomes obvious (as it must total 9).                

To multiply 8 x 9  

Deduct 1 from the 8 = 7 (this is the first number of the answer)

The numbers in the answer always total 9 so the second number must be 2     

Therefore 8 x 9 =72

a:  Add together the digits you are multiplying  e.g. 33 x 11 add the 3 + 3 =6

b:  Place the the answer in between the two digits  e.g.   363

Therefore 33 x 11 = 363

If the two digits add up to more than ten (e.g. 48 x 11 where 4+8=12) then you have to add the 1 to the 4 and place the 2 in the middle of the two numbers. 

Therefore 48 x 11 = 528

If you ever need to find out the sum of all the numbers between two given digits, here is the formula :-

ADD TOGETHER THE FIRST NUMBER AND THE LAST NUMBER IN THE SEQUENCE THEN MULTIPLY BY THE NUMBER OF THE MIDDLE NUMBER IN THE SEQUENCE.

I will try to explain - say you wanted to find out the total of numbers 7 through to 35.

i.e. 7+8+9 +10+11 an so on until..33+34+35.

First add the first number in the sequence to the last number in the sequence, which in this case is -  7 + 35 = 42

Then to find the NUMBER of the middle digit in the sequence you deduct the lowest number from the highest number, add 1 then divide by 2

i.e.  35 - 7 = 28 + 1 = 29 divided by 2 =14.5

NOW MULTIPLY 42 X 14.5 = 609

SO THE SUM OF ALL FIGURES BETWEEN 7 AND 35 = 609

---

Now all you accountants out there - give us some more (or have you forgotten them!) - contact us on june@hintsandthings.co.uk.

For more mathematical shortcuts click here.