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what is 287 * 326
 Jun 16, 2022

Best Answer 

 #1
avatar+514 
+3

\(287\cdot \:326=93562\)

\(Line\:up\:the\:numbers\)

\(\begin{matrix}\:\:&2&8&7\\ \times \:&3&2&6\end{matrix}\)

\(Multiply\:the\:top\:number\:by\:the\:bottom\:number\:one\:digit\:at\:a\:time\:starting\:with\:the\:ones\:digit\:\left(from\:right\:to\:left\right) \)

 

\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)

\(\begin{matrix}\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \times \:&3&2&\textbf{6}\end{matrix}\)

\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:6=42\)

\(\mathrm{Carry\:}4\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&4&\:\:\\ \:\:&2&8&\textbf{7}\\ \times \:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&\:\:&2\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:4+8\cdot \:6=52\)

\(\mathrm{Carry\:}5\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&5&\textbf{4}&\:\:\\ \:\:&2&\textbf{8}&7\\ \times \:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&2&2\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:5+2\cdot \:6=17\)

\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}7\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&1&\textbf{5}&4&\:\:\\ \:\:&\:\:&\textbf{2}&8&7\\ \times \:&\:\:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&7&2&2\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:digit,\:}1\mathrm{,\:to\:the\:result}\)

\(\frac{\begin{matrix}\:\:&1&5&4&\:\:\\ \:\:&\:\:&2&8&7\\ \times \:&\:\:&3&2&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\end{matrix}}\)

\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)

\(\frac{\begin{matrix}\:\:&\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\end{matrix}}\)

\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:2=14\)

\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}4\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&1&\:\:\\ \:\:&\:\:&2&8&\textbf{7}\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&\:\:&\:\:&4&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+8\cdot \:2=17\)

\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}7\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&1&\textbf{1}&\:\:\\ \:\:&\:\:&2&\textbf{8}&7\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&\:\:&7&4&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+2\cdot \:2=5\)

\(\frac{\begin{matrix}\:\:&\:\:&\textbf{1}&1&\:\:\\ \:\:&\:\:&\textbf{2}&8&7\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&5&7&4&\:\:\end{matrix}}\)

\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)

\(\frac{\begin{matrix}\:\:&\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&5&7&4&\:\:\end{matrix}}\)

\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:3=21\)

\(\mathrm{Carry\:}2\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}1\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&\:\:&2&\:\:\\ \:\:&\:\:&\:\:&2&8&\textbf{7}\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&\:\:&\:\:&1&\:\:&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:2+8\cdot \:3=26\)

\(\mathrm{Carry\:}2\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}6\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&2&\textbf{2}&\:\:\\ \:\:&\:\:&\:\:&2&\textbf{8}&7\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&\:\:&6&1&\:\:&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:2+2\cdot \:3=8\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&\textbf{2}&2&\:\:\\ \:\:&\:\:&\:\:&\textbf{2}&8&7\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&8&6&1&\:\:&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:rows\:to\:get\:the\:answer.\:\:For\:simplicity,\:fill\:in\:trailing\:zeros\:}\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&2&8&7\\ \:\:&\:\:&\times \:&3&2&6\end{matrix}}{\begin{matrix}\:\:&0&1&7&2&2\\ \:\:&0&5&7&4&0\\ \:\:&8&6&1&0&0\end{matrix}}\)

\(=93562\)

.
 Jun 16, 2022
 #1
avatar+514 
+3
Best Answer

\(287\cdot \:326=93562\)

\(Line\:up\:the\:numbers\)

\(\begin{matrix}\:\:&2&8&7\\ \times \:&3&2&6\end{matrix}\)

\(Multiply\:the\:top\:number\:by\:the\:bottom\:number\:one\:digit\:at\:a\:time\:starting\:with\:the\:ones\:digit\:\left(from\:right\:to\:left\right) \)

 

\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)

\(\begin{matrix}\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \times \:&3&2&\textbf{6}\end{matrix}\)

\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:6=42\)

\(\mathrm{Carry\:}4\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&4&\:\:\\ \:\:&2&8&\textbf{7}\\ \times \:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&\:\:&2\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:4+8\cdot \:6=52\)

\(\mathrm{Carry\:}5\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&5&\textbf{4}&\:\:\\ \:\:&2&\textbf{8}&7\\ \times \:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&2&2\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:5+2\cdot \:6=17\)

\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}7\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&1&\textbf{5}&4&\:\:\\ \:\:&\:\:&\textbf{2}&8&7\\ \times \:&\:\:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&7&2&2\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:digit,\:}1\mathrm{,\:to\:the\:result}\)

\(\frac{\begin{matrix}\:\:&1&5&4&\:\:\\ \:\:&\:\:&2&8&7\\ \times \:&\:\:&3&2&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\end{matrix}}\)

\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)

\(\frac{\begin{matrix}\:\:&\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\end{matrix}}\)

\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:2=14\)

\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}4\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&1&\:\:\\ \:\:&\:\:&2&8&\textbf{7}\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&\:\:&\:\:&4&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+8\cdot \:2=17\)

\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}7\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&1&\textbf{1}&\:\:\\ \:\:&\:\:&2&\textbf{8}&7\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&\:\:&7&4&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+2\cdot \:2=5\)

\(\frac{\begin{matrix}\:\:&\:\:&\textbf{1}&1&\:\:\\ \:\:&\:\:&\textbf{2}&8&7\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&5&7&4&\:\:\end{matrix}}\)

\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)

\(\frac{\begin{matrix}\:\:&\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&5&7&4&\:\:\end{matrix}}\)

\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:3=21\)

\(\mathrm{Carry\:}2\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}1\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&\:\:&2&\:\:\\ \:\:&\:\:&\:\:&2&8&\textbf{7}\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&\:\:&\:\:&1&\:\:&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:2+8\cdot \:3=26\)

\(\mathrm{Carry\:}2\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}6\mathrm{\:in\:the\:result\:line}\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&2&\textbf{2}&\:\:\\ \:\:&\:\:&\:\:&2&\textbf{8}&7\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&\:\:&6&1&\:\:&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:2+2\cdot \:3=8\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&\textbf{2}&2&\:\:\\ \:\:&\:\:&\:\:&\textbf{2}&8&7\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&8&6&1&\:\:&\:\:\end{matrix}}\)

\(\mathrm{Add\:the\:rows\:to\:get\:the\:answer.\:\:For\:simplicity,\:fill\:in\:trailing\:zeros\:}\)

\(\frac{\begin{matrix}\:\:&\:\:&\:\:&2&8&7\\ \:\:&\:\:&\times \:&3&2&6\end{matrix}}{\begin{matrix}\:\:&0&1&7&2&2\\ \:\:&0&5&7&4&0\\ \:\:&8&6&1&0&0\end{matrix}}\)

\(=93562\)

mworkhard222 Jun 16, 2022
 #2
avatar+118118 
+1

Impressive presentation mworkhard222  !!!

 

 

Just playing with numbers, here is another way.

 

 287 * 326

                [ 3*326 = 900+60+18 = 978]

= 300*326-10*326-3*326 

=  97800 - 978 - 3260

= 94800 - 978 - 260

= 83700 - 78 - 60

= 83700 - 138

= 83700 - 200+62

=83562

Melody  Jun 17, 2022

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