Multiplying together numbers near 50

Multiplying numbers near 50 is very similar to the useful procedure for multiplying numbers near 100. Note that the answers to problems of this type will be near 50×50=2500, not 100×100=10000. Also, 50 is half 100 so this must be accounted for when deriving the first two digits of the answer.

 

To multiply numbers near to but less than 50, first subtract the numbers being multiplied from 50.

-If the differences are an even/even pair or an odd/odd pair:     ex.   46×48=2208

—–Multiply the differences to yield the last two digits of the answer.                                                                      ex.  50-46=4                         50-48=2                          4×2=_ _ 08

—–Add the differences and half this figure. Subtract this half from 25 to yield the first two digits of the answer.    ex.   (4+2)/2=3                                 25-3=22_ _

-If the differences are an odd/even pair:      ex.   47×44=2068

—–Multiply the differences and add 50 to yield the last two digits of the answer.                                        ex.   50-47=3                         50-44=6                    (6×3)+50= _ _ 68

—–Add the differences and half, rounding up the answer. Subtract this rounded up half                from 25 to yield the first two digits of the answer.  ex.   (3+6)/2=5             25-5=20 _ _

 

To multiply numbers near to but greater than 50, first subtract the numbers being multiplied from 50.     ex. for  52×54=2808      52-50=2       54-50=4                                                                                                 for  53×56=2968      53-50=3        56-50=6

-Follow step one above for multiplying the different kinds of digit pairs. This yields the last two digits of the answer.     ex.   for 52×54=2808         2×4=_ _08                                                                                                                 for 53×56=2968        (3×6)+50=_ _68

-Add the differences and half, rounding down this figure if it is not even. Add this figure to 25 to yield the first two digits of the answer.   ex.  for 52×54=2808   (2+4)/2=3     25+3=28_ _                                             for 53×56=2968   (3+6)/2=4     25+4=29_ _

 

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