Chap 5 Algebra: An Application of Distributive Law

Refer to Brainworks (in textbook p103) - It shows an example how distributive law could be used to 'simplify' complex arithmetic:

37 x 99
= 37 x (100 - 1)
= 37x100 - 37x1
= 3700 - 37
= 3663

Devise ONE arithmetic problem that you could illustrate how distributive law could be applied to simplify the solving process.
Enter your "arithmetic problem & solution" in comments.

23 comments:

  1. 36 x 101
    = 36 x (100 + 1)
    = (36 x 100) + (36 x 1)
    = 3600 + 36
    = 3636

    ReplyDelete
  2. 78 x 103 = 78 x (100+3)
    = 7800 + 234
    = 834

    ReplyDelete
  3. 38 x 199
    = 38 x (200 - 1)
    = (38 x 200) - (38 x 1)
    = 7600 - 38
    = 7562

    ReplyDelete
  4. 50 x 22
    = 50 x (20+2)
    = 50 x 20 + 50 x 2
    = 1000 + 100
    = 1100

    ReplyDelete
  5. 36 x 101
    = 36 x (100 + 1)
    = (36 x 100) + (36 x 1)
    = 3600 + 36
    = 3636

    ReplyDelete
  6. 60 x 48
    = 60 x ( 50 -2 )
    = 60 x 50 - 60 x 2
    = 3000 - 120
    = 2880

    ReplyDelete
  7. 72 x 102
    =72 x ( 100+2)
    = 7200+ 144
    = 7344

    ReplyDelete
  8. 104x99
    =104x(100-1)
    =10400-104
    =10296

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  9. 78x103
    = 78x (100+3)
    = 1800 + (78x3)
    = 1800+234
    = 2034

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  10. 97 x 101
    = 97 x (100 + 1)
    = 97 x 100 + 97 x 1
    = 9700 + 97
    = 9797

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  11. 22 x 98
    = 22 x (100 - 2)
    = 22 x 100 - 22 x 2
    = 2200 - 44
    = 2156

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  12. 9999 x 9999
    = 9999 x (10000 - 1)
    = 9999 x 10000 - 9999 x 1
    = 99990000 - 9999
    = 99980001

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  13. To all who have submitted so far... Well done :)

    The rest... waiting for your examples...

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  14. 31x41
    =31x(40+1)
    =31x40+31x1
    =1240+31
    =1271

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  15. 678 x 99
    = 678 x (100 - 1)
    =678 x 100 - 678 x 1
    =67800 - 678
    =67100

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  16. 374 x 61
    =374 x 50 + 374 x 10 + 374
    =18700 + 3740 + 374
    = 22 814

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  17. 170 x 710
    =170 x (700+10)
    =119000 + (10 x 170)
    =119000 + 1700
    =120700

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  18. 100x239
    =100x(240-1)
    =100x240-100x1
    =24000-100
    =23900

    ReplyDelete
  19. This comment has been removed by the author.

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  20. This comment has been removed by the author.

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  21. 98 x 102
    = 98 x (100+2)
    = 98 x 100 + 98 x 2
    = 9800+ 196
    =9996

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  22. This comment has been removed by the author.

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  23. The 6th additional posts are fine too :)

    One for discussion: Grace's example -
    170 x 710
    = 170 x (700+10)
    = 119000 + (10 x 170)

    Would be good to further 'breakdown' in the process so that we deal with 'smaller' numbers first. Can consider:
    170 x 710
    = 170 x (700+10)
    = 170x700 + 170x10
    = 170x7x100 + 1700
    = 1190x100 + 1700
    = ....

    On the other hand, it's not so common to use distributive law on numbers that are not near the 'hundreds'

    ReplyDelete