Multiplying together numbers near 50 and 100

To multiply numbers below and near 50 times numbers below and near 100:

-Subtract these numbers from their base numbers of 50 or 100 and multiply together these figures to obtain the last two digits of the answer.  If the difference of 100 and the number close to 100 is odd, add 50 to the answer.

ex.   99×44=4356   100-99=1, which is odd   50-44=6    (6×1)+50=_ _ 56                                          ex.   96×46=4416          100-96=4                 50-46=4                  4×4=_ _16

-Take the figures that were multiplied above. Add together half the number subtracted from 100 (rounding up any fraction) and the number subtracted from 50. Subtract this from 50 to yield the first two numbers of the answer.   ex. for 99×44=4356        1+6=7        50-7=43_ _                                                                              ex. for 96×46=4416    (4)/2+4=6    50-6=44_ _

Prove these:    95×45=4275         94×48=4512          91×46=4186

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