(a) 44 ÷ 2 + (7 + 80 ÷ 10) – 14 + 23 (Given)

= 44 ÷ 2 + (7 + 8) – 14 + 23 (To complete the bracket ÷ done first) 

= 44 ÷ 2 + 15 – 14 + 23 (Bracket completed second) 

= 22 + 15 – 14 + 23 (÷ completed third) 

= 37 – 37 (+ completed fourth) 

= 0 (- completed last) 

∴ 44 ÷ 2 + (7 + 80 ÷ 10) – 14 + 23 = 0.

(b) 17 x 6 – 4 – 2 + 20 – (22 + 18) (Given) 

= 17 x 6 – 4 – 2 + 20 – 40 (Bracket completed first) 

= 102 – 4 – 2 + 20 – 40 (x completed second) 

= 102 – 4 – 22 – 40 (+ completed third) 

= 98 – 22 – 40 (÷ completed one by one) 

= 76 – 40 

= 36 

∴ 17 x 6 – 4 – 2 + 20 – (22 + 18) = 36

(c) 16 x 144 ÷ 16 ÷ 9 + 16 + 15 – 20 (Given) 

= 16 x 9 ÷ 9+16 + 15 – 20 (÷ completed first) 

= 16 x 1 + 16 + 15 – 20 (÷ completed second) 

= 16 + 16 + 15 – 20 (x completed third) 

= 32 + 15 – 20 (+ completed fourth) 

= 47 – 20 (+ completed fifth) 

= 27 (- completed last) 

∴ 16 x 144 ÷ 16 ÷ 9 + 16 + 15 – 20 = 27

(d) 12 x 36 ÷ 12 ÷ 3 + 5 + 6 – 2 (Given) 

= 12 x 3 ÷ 3 + 5 + 6 – 2 (÷ completed first) 

= 12 x 1 + 5 + 6 – 2 (÷ completed second) 

= 12 + 5 + 6 – 2 (x completed third) 

= 17 + 6 – 2 (+ completed forth) 

= 23 – 2 (+ completed fifth) 

= 21 (- completed last) 

∴ 12 x 36 ÷ 12 ÷ 3 + 5 + 6 – 2 = 21

(e) 15 – [17 + 30 ÷ 6 – (6 + 6) + 7] (Given) 

= 15 – [17 + 30 ÷ 6 – 12 + 7] (Inner bracket completed first) 

= 15 – [17 + 5 – 12 + 7] (÷ completed second) 

= 15 – [22 – 19] (+ completed third) 

= 15 – 3 (bracket completed forth) 

= 12 (- completed last) 

∴ 15 – [17 + 30 ÷ 6 – (6 + 6) + 7] = 12.