question_answer 9)

Use the sign of >, < or = in the box to make the statements true. (d)\[\left( -8 \right)+\left( -4 \right)\]     \[\]\[\left( -8 \right)-\left( -4 \right)\] (b) \[\left( -\text{3} \right)+\text{7}-\left( \text{19} \right)\]\[\] \[15-8+(-9)\] (c) \[~\text{23}-\text{41}+\text{11}\]\[\]\[\text{23}-\text{41}-\text{11}\] (d) \[\text{39}+\left( -\text{24} \right)-\left( \text{15} \right)\]\[\]\[~\text{36}+\left( -\text{52} \right)-\left( -\text{36} \right)\] (e) \[~-\text{ 231}+\text{79}+\text{51}\]\[\]\[~-\text{ 399}+\text{159}+\text{81}\].                

Answer:

                (a) L.H.S \[=(-8)+(-4)=-(8+4)=-12\] R.H.S. \[=(-8)-(-4)=-8+4=-(8-4)~=-\text{ }4\] \[\therefore \] \[\left( -8 \right)+\left( -4 \right)\left( -8 \right)-\left( -4 \right)\] (b)  L.H.S. \[=\left( -\text{3} \right)+\text{7}-\left( \text{19} \right)=+\text{ 4}-\left( \text{19} \right)\] \[=+\,4-19=-15\] R.H.S. \[=\text{15}-\text{8}+\left( -\text{ 9} \right)=\text{7}+\left( -\text{ 9} \right)\] \[=\text{7}-\text{9}=-\text{2}\] \[\therefore \] \[~\left( -\text{3} \right)+\text{7}-\left( \text{19} \right)\]\[\]\[\text{15}-\text{8}+\left( -\text{9} \right)\] (c) \[\text{L}.\text{H}.\text{S}.\text{ }=\text{23}-\text{41}+\text{11}=\text{23}+\text{11}-\text{41}\] \[=\text{34}-\text{41}=-\left( \text{41}-\text{34} \right)=-\text{ 7}\] R.H.S. \[=\text{23}-\text{41}-\text{11}=\text{23}-\left( \text{41}+\text{11} \right)\] \[=\text{23}-\text{52}=-\left( \text{52}-\text{23} \right)=-\text{ 29}\] \[\therefore \] \[\text{23}-\text{41}+\text{11}\text{ 23}-\text{41}-\text{11}\] (d) L.H.S. \[=\text{39}+\left( -\text{ 24} \right)-\left( \text{15} \right)=\text{39}-\text{24}-\left( \text{15} \right)\]\[=\text{15}-\left( \text{15} \right)=0\] R.H.S. \[=\text{36}+\left( -\text{ 52} \right)-\left( -\text{ 36} \right)=-\left( \text{52}-\text{36} \right)\]\[-\]\[\left( -\text{36} \right)\text{ }=\]\[-\text{16}-\left( -\text{ 36} \right)\]\[=-\text{ 16}+\text{36}=\text{2}0\] \[\therefore \]  \[~\text{39}+\left( -\text{24} \right)-\left( \text{15} \right)\text{ }\]\[\text{36}+\left( -\text{52} \right)\]\[-\left( -\text{36} \right)\] (e)  L.H.S. \[~=-\text{231}+\text{79}+\text{51}=-\text{231}+\text{13}0\]\[~=-\left( \text{231}-\text{13}0 \right)=-\text{1}0\text{1}\] R.H.S. \[~=-\text{399}+\text{159}+\text{81}=-\text{399}+\text{24}0\]\[=-\left( \text{399}-\text{24}0 \right)=-\text{159}\] \[\therefore \] \[-\text{ 231}+\text{79}+\text{51}\] \[\]\[~-\text{ 399 }+\text{159}+\text{81}.\]