question_answer 15)

Find each of the following products: (a) \[~\text{3}\times (-\text{1})\]                            (b) \[\text{(}-\text{1)}\times \text{225}\]                            (c) \[\text{(}-\text{21)}\times (-\text{ 3}0)\]             (d) \[\text{(}-\text{316)}\times (-\text{ 1})\] (e) \[\text{(}-\text{15)}\times 0\times (-\text{l8})\]        (f) \[(-\text{12})\times (-11)\times (\text{1}0)\]                (g) \[\text{9}\times (-\text{ 3})\times (-\text{ 6})\]         (h) \[\text{(}-\text{l 8)}\times (-\text{ 5})\times (-\text{ 4})\] (i) \[\text{(}-\text{1)}\times (-\text{ 2})\times (-\text{ 3})\times \text{4}\]                                          (j) \[\text{(}-\text{3)}\times (-\text{ 6})\times (-\text{ 2})\times (-\text{1})\].                

Answer:

                 (a) \[\text{3}\times (-\text{l})\] \[\text{3}\times (-\text{ 1})=-(\text{3}\times 1)=-\text{3}.\] (b) \[(-1)\times 225\] \[\text{(}-\text{l)}\times \text{225}=-\left( \text{1}\times \text{225} \right)=-\text{225}.\] (c) \[(-21)\times (-30)\] \[\text{(}-\text{21)}\times (-\text{ 3}0)=\text{21}\times \text{3}0=\text{63}0.\] (d) \[(-316)\times (-1)\] \[\text{(}-\text{316)}\times (-\text{ l})=\text{316}\times \text{l}=\text{316}.\] (e) \[(-15)\times 0\times (-18)\] \[\text{(}-\text{15)}\times 0\times \text{(}-\text{18)}=\{(-\text{ 15})\times 0\}\times (-\text{ 18})\] \[~=0\times (-\text{ 18})=0\]. (f) \[(-12)\times (-11)\times 10\] \[~=\left( \text{12}\times \text{11} \right)\times \text{1}0\] \[=\text{132}\times \text{1}0=\text{132}0.\] (g) \[9\times (-\mathbf{ }3)\times (-6)\] \[\text{9}\times (-\text{ 3})\times (-\text{ 6})=\text{9}\times \text{ }\!\![\!\!\text{ (}-\text{ 3)}\times (-\text{ 6})\text{ }\!\!]\!\!\text{ }\] \[=\text{9}\times (\text{3}\times \text{6})=\text{9}\times \text{18}=\text{162}.\] (h) \[(-18)\times (-\mathbf{ }5)\times (-4)\] \[\text{(}-\text{18)}\times (-\text{ 5})\times (-\text{ 4})=[(-\text{ 18})\times (-\text{ 5})]\times (-\text{ 4})\] \[~=(\text{18}\times \text{5})\times (-\text{ 4})=-\text{ (9}0\times \text{4)}=-\text{ 36}0.\] (i) \[(-1)\times (-2)\times (-3)\times 4\] \[=[(-\text{ 1})\times (-\text{ 2})]\times [(-\text{ 3})\times \text{4}]\] \[~=(\text{1}\times \text{2})\times [-(\text{3}\times \text{4})]\] \[=\text{2}\times [-(\text{12})]=\text{2}\times (-\text{12})=-(\text{2}\times \text{12})=-\text{24}.\] (j) \[(-3)\times (-6)\times (-2)\times (-1)\] \[\text{(}-\text{3)}\times (-\text{6})\times (-\text{2})\times (-\text{1})\] \[=[(-\text{3})\times (-\text{6})]\times [(-\text{2})\times (-\text{1})]\] \[=(\text{3}\times \text{6})\times (\text{2}\times \text{1})=\text{18}\times \text{2}=\text{36}.\]