Question

Determine the sum by suitable rearrangements:

(i) 953+407+647
(ii) 15409+178+591+322
(iii) 2359+10001+2641+9999
(iv) 1+2+3+4+1996+1997+1998+1999
(v) 10+11+12+13+14+15+16+17+18+19+20

Answer 1

(i) 953 + 407 + 647
∵ 53 + 47 = 100
∴ (953 + 647) + 407 = 1600 + 407 = 2007

(ii) 15409 + 178 + 591 + 322
∵ 409 + 91 = 500
and
78+22 = 100
∴ (15409 + 591) + (178 + 322)
= (16000) + (500)
= 16500

(iii) 2359 + 10001 + 2641 + 9999
∵ 59 + 41 = 100
and
99 + 01 = 100
∴ (2359 + 2641) + (10001 + 9999)
= (5000) + (20000)
= 25000

(iv) 1 + 2 + 3 + 4 + 1996 + 1997 + 1998 + 1999
∵ 99 + 1 = 100
98 + 2 = 100
97 + 3 = 100
and
96 + 4 = 100
∴ (1 + 1999) + (2 + 1998) + ( 3 + 1997) + (4 + 1996)
= 2000 + 2000 + 2000 + 2000
= 8000

(v) 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20
∵ 10 + 20 = 30
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
and
4 + 6 = 10
∴ (10 + 20) + (11 + 19) + (12 + 18) + (13 + 17) + (14 + 16) + 15
= 30 + 30 + 30 + 30 + 30 + 15
= 150 + 15
= 165