USING SUITABLE REARRANGEMENT AND FIND THE SUM OF INTEGERS
Two numbers that add together are called complements.
- 12 and 8 are complements to 20 because 12 + 8 = 20
- 35 and 65 are complements to 100 because 35 + 65 = 100
Like this, we can get many combinations.
Problem 1 :
31 + 32 + 33 + 34 + 35 + 65 + 66 + 67 + 68 + 69
Solution :
31 + 32 + 33 + 34 + 35 + 65 + 66 + 67 + 68 + 69
By observing the given integers, we can find complements.
= (31 + 69) + (32 + 68) + (33 + 67) + (34 + 66) + (35 + 65)
= 100 + 100 + 100 + 100 + 100
= 500
Problem 2 :
1 + 2 + 3 + 4 + 996 + 997 + 998 + 999
Solution :
= 1 + 2 + 3 + 4 + 996 + 997 + 998 + 999
= (1 + 999) + (2 + 998) + (3 + 997) + (4 + 996)
= 1000 + 1000 + 1000 + 1000
= 4000
Problem 3 :
12 + 14 + 16 + 18 + 20 + 80 + 82 + 84 + 86 + 88
Solution :
= 12 + 14 + 16 + 18 + 20 + 80 + 82 + 84 + 86 + 88
= (12 + 88) + (14 + 86) + (16 + 84) + (18 + 82) + (20 + 80)
= 100 + 100 + 100 + 100 + 100
= 500
Problem 4 :
8 + 259 + 92
Solution :
= 8 + 259 + 92
= (8 + 92) + 259
= 100 + 259
= 359
Problem 5 :
137 + 269 + 63
Solution :
= 137 + 269 + 63
= (137 + 63) + 269
= 200 + 269
= 469
Problem 6 :
987 + 241 + 159
Solution :
= 987 + 241 + 159
= 987 + 200 + 41 + 100 + 59
= 987 + (200 + 100) + (41 + 59)
= 987 + 300 + 100
= 900 + 87 + 300 + 100
= (900 + 100) + 300 + 87
= 1000 + 300 + 87
= 1387
Problem 7 :
163 + 979 + 21
Solution :
= 163 + 979 + 21
= 100 + 63 + 900 + (79 + 21)
= (100 + 900) + 63 + (79 + 21)
= 1000 + 100 + 63
= 1163
Problem 8 :
567 + 167 + 33
Solution :
= 567 + 167 + 33
= 500 + 67 + 100 + 67 + 33
= (500 + 100) + 67 + (67 + 33)
= 600 + 100 + 67
= 700 + 67
= 767
Problem 9 :
364 + 779 + 636
Solution :
= 364 + 779 + 636
= (300 + 64) + (700 + 79) + (600 + 36)
= (300 + 700 + 600) + (64 + 36 + 79)
= 1600 + 179
= 1779
Problem 10 :
978 + 777 + 22
Solution :
= 978 + 777 + 22
= 900 + (78 + 22) + 777
= 900 + 100 + 777
= 1000 + 777
= 1777
Problem 11 :
99 + 899 + 1901
Solution :
= 99 + 899 + 1901
= 99 + 800 + 99 + 1900 + 1
= 1900 + (99 + 1) + 99 + 800
= 1900 + 100 + 99 + 800
= 2000 + 800 + 99
= 2800 + 99
= 2899
Problem 12 :
89 + 75 + 25 + 11
Solution :
= 89 + 75 + 25 + 11
= (89 + 11) + (75 + 25)
= 100 + 100
= 200
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