SOLUTION: Mentally compute the product of 49 and 19. Describe the steps that you mentally went through to get your answer. Prove your answer using standard multiplication. Show your work.

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Question 1084467: Mentally compute the product of 49 and 19. Describe the steps that you mentally went through to get your answer. Prove your answer using standard multiplication. Show your work.
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
Based on an identity (x-1)*(y-1) = xy - (x+y) + 1, substitute x= 50, y= 20 and do this:


1.  Calculate 50*20 = 1000 (mentally).


2.  Calculate 50 + 20 = 70 (mentally).


3.  Subtract 70 from 1000 to get 930 (mentally).


4.  Finally, add 1 to 930 to get 931 (mentally).

Done.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Mentally compute the product of 49 and 19. Describe the steps that you mentally went through to get your answer.
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There's more than 1 way.
The average is (49+19)/2 = 34
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The difference from the average is 15
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49*19 = 34^2 - 15^2 = 1156 - 225 = 931
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Or,
50*19 = 950
950 - 19 = 931
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Or 49*19 = 7*7*19 = 7*133 = 931
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How is my way of doing it relevant?
How would you do it?
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