### 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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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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'