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MATHEMATICAL SHORTCUTSHandy shortcuts for checking calculations, without the need of a calculator! To check addition is correct -
To check subtraction is correct:-
To check multiplication is correct:-
To check division is correct:-
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): 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 Now for the 11 times table - 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.
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