question_answer 14)

Find the sum of (a) 137 and ? 354 (b) ?52 and 52 (c) ?312, 39 and 192 (d) ?50, ?200 and 300

Answer:

(a) We have, \[137+(-354)=137+(-137)+(-217)\] \[[\because 354=137+217\Rightarrow -354\text{ }=-137+-217]\] \[=0+(-217)=-217[\because 137+(-137)=0]\] (b) We have, \[-52+(+52)=0\] (c) We have, \[-312+39+192=-312+231=(-231)+(-81)+231\]\[[\because 312=231+81\Rightarrow -312=-231+(-81)]\] \[=(-231)+231+(-81)\] \[=0+(-81)=-81[\because (-231)+231=0]\] (d) We have, \[(-50)+(-200)+(300)=-(50+200)+300\] \[=(-250)+(300)\]\[[\because 300+250+50]\] \[=(-250)+(250)+(50)\] \[=0+50=50\] \[[\because (-250)+(250)=0]\]