question_answer 1)

Add without using number line: (a) 11 + (?7) (b) (?13) + (+18) (c) (?10) + (+19) (d) (?250) + (+150) (e) (?380) + (?270) (f) (?217) + (?100)

Answer:

(a) We have, \[11+(-7)=(+4)+(+7)+(-7)\] \[[\because 11=4+7]\]\[=(+4)+(0)=4\] \[[\because (+7)+(-7)=0]\] (b) We have, \[(-13)+(+18)=(-13)+(+13)+(5)\] \[[\because 18=13+5]\] \[=0+(+5)=5\] \[[\because (-13)+(+13)=0]\] (c) We have, \[(-10)+(+19)=(-10)+(+10)+(9)\] \[[\because 19=10+9]\] \[=0+(+9)=9\] \[[\because (-10)+(+10)=0]\] (d) We have, \[(-250)+(+150)=(-150)+(-100)+(+150)\] \[[\because 250=150+100\Rightarrow -250=-150+(-100)]\] \[=(-150)+(+150)+(-100)\] \[=0+(-100)=-100[\because (-150)+(=150)=0]\] (e) We have, \[(-380)+(-270)=-(380+270)=-650\] (f) We have, \[(-217)+(-100)=-(217+100)=-317\]