+515 \(287\cdot \:326=93562\)
\(Line\:up\:the\:numbers\)
\(\begin{matrix}\:\:&2&8&7\\ \times \:&3&2&6\end{matrix}\)
\(Multiply\:the\:top\:number\:by\:the\:bottom\:number\:one\:digit\:at\:a\:time\:starting\:with\:the\:ones\:digit\:\left(from\:right\:to\:left\right) \)
\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)
\(\begin{matrix}\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \times \:&3&2&\textbf{6}\end{matrix}\)
\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:6=42\)
\(\mathrm{Carry\:}4\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&4&\:\:\\ \:\:&2&8&\textbf{7}\\ \times \:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&\:\:&2\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:4+8\cdot \:6=52\)
\(\mathrm{Carry\:}5\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&5&\textbf{4}&\:\:\\ \:\:&2&\textbf{8}&7\\ \times \:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&2&2\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:5+2\cdot \:6=17\)
\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}7\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&1&\textbf{5}&4&\:\:\\ \:\:&\:\:&\textbf{2}&8&7\\ \times \:&\:\:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&7&2&2\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:digit,\:}1\mathrm{,\:to\:the\:result}\)
\(\frac{\begin{matrix}\:\:&1&5&4&\:\:\\ \:\:&\:\:&2&8&7\\ \times \:&\:\:&3&2&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\end{matrix}}\)
\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)
\(\frac{\begin{matrix}\:\:&\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\end{matrix}}\)
\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:2=14\)
\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}4\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&1&\:\:\\ \:\:&\:\:&2&8&\textbf{7}\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&\:\:&\:\:&4&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+8\cdot \:2=17\)
\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}7\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&1&\textbf{1}&\:\:\\ \:\:&\:\:&2&\textbf{8}&7\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&\:\:&7&4&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+2\cdot \:2=5\)
\(\frac{\begin{matrix}\:\:&\:\:&\textbf{1}&1&\:\:\\ \:\:&\:\:&\textbf{2}&8&7\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&5&7&4&\:\:\end{matrix}}\)
\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)
\(\frac{\begin{matrix}\:\:&\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&5&7&4&\:\:\end{matrix}}\)
\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:3=21\)
\(\mathrm{Carry\:}2\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}1\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&\:\:&2&\:\:\\ \:\:&\:\:&\:\:&2&8&\textbf{7}\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&\:\:&\:\:&1&\:\:&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:2+8\cdot \:3=26\)
\(\mathrm{Carry\:}2\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}6\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&2&\textbf{2}&\:\:\\ \:\:&\:\:&\:\:&2&\textbf{8}&7\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&\:\:&6&1&\:\:&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:2+2\cdot \:3=8\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&\textbf{2}&2&\:\:\\ \:\:&\:\:&\:\:&\textbf{2}&8&7\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&8&6&1&\:\:&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:rows\:to\:get\:the\:answer.\:\:For\:simplicity,\:fill\:in\:trailing\:zeros\:}\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&2&8&7\\ \:\:&\:\:&\times \:&3&2&6\end{matrix}}{\begin{matrix}\:\:&0&1&7&2&2\\ \:\:&0&5&7&4&0\\ \:\:&8&6&1&0&0\end{matrix}}\)
\(=93562\)
.+515 \(287\cdot \:326=93562\)
\(Line\:up\:the\:numbers\)
\(\begin{matrix}\:\:&2&8&7\\ \times \:&3&2&6\end{matrix}\)
\(Multiply\:the\:top\:number\:by\:the\:bottom\:number\:one\:digit\:at\:a\:time\:starting\:with\:the\:ones\:digit\:\left(from\:right\:to\:left\right) \)
\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)
\(\begin{matrix}\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \times \:&3&2&\textbf{6}\end{matrix}\)
\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:6=42\)
\(\mathrm{Carry\:}4\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&4&\:\:\\ \:\:&2&8&\textbf{7}\\ \times \:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&\:\:&2\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:4+8\cdot \:6=52\)
\(\mathrm{Carry\:}5\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&5&\textbf{4}&\:\:\\ \:\:&2&\textbf{8}&7\\ \times \:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&2&2\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:5+2\cdot \:6=17\)
\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}7\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&1&\textbf{5}&4&\:\:\\ \:\:&\:\:&\textbf{2}&8&7\\ \times \:&\:\:&3&2&\textbf{6}\end{matrix}}{\begin{matrix}\:\:&\:\:&7&2&2\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:digit,\:}1\mathrm{,\:to\:the\:result}\)
\(\frac{\begin{matrix}\:\:&1&5&4&\:\:\\ \:\:&\:\:&2&8&7\\ \times \:&\:\:&3&2&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\end{matrix}}\)
\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)
\(\frac{\begin{matrix}\:\:&\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\end{matrix}}\)
\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:2=14\)
\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}4\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&1&\:\:\\ \:\:&\:\:&2&8&\textbf{7}\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&\:\:&\:\:&4&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+8\cdot \:2=17\)
\(\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}7\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&1&\textbf{1}&\:\:\\ \:\:&\:\:&2&\textbf{8}&7\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&\:\:&7&4&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+2\cdot \:2=5\)
\(\frac{\begin{matrix}\:\:&\:\:&\textbf{1}&1&\:\:\\ \:\:&\:\:&\textbf{2}&8&7\\ \:\:&\times \:&3&\textbf{2}&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&5&7&4&\:\:\end{matrix}}\)
\(\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}\)
\(\frac{\begin{matrix}\:\:&\:\:&\textbf{2}&\textbf{8}&\textbf{7}\\ \:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&1&7&2&2\\ \:\:&5&7&4&\:\:\end{matrix}}\)
\(\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:7\cdot \:3=21\)
\(\mathrm{Carry\:}2\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}1\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&\:\:&2&\:\:\\ \:\:&\:\:&\:\:&2&8&\textbf{7}\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&\:\:&\:\:&1&\:\:&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:2+8\cdot \:3=26\)
\(\mathrm{Carry\:}2\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}6\mathrm{\:in\:the\:result\:line}\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&2&\textbf{2}&\:\:\\ \:\:&\:\:&\:\:&2&\textbf{8}&7\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&\:\:&6&1&\:\:&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:2+2\cdot \:3=8\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&\textbf{2}&2&\:\:\\ \:\:&\:\:&\:\:&\textbf{2}&8&7\\ \:\:&\:\:&\times \:&\textbf{3}&2&6\end{matrix}}{\begin{matrix}\:\:&\:\:&1&7&2&2\\ \:\:&\:\:&5&7&4&\:\:\\ \:\:&8&6&1&\:\:&\:\:\end{matrix}}\)
\(\mathrm{Add\:the\:rows\:to\:get\:the\:answer.\:\:For\:simplicity,\:fill\:in\:trailing\:zeros\:}\)
\(\frac{\begin{matrix}\:\:&\:\:&\:\:&2&8&7\\ \:\:&\:\:&\times \:&3&2&6\end{matrix}}{\begin{matrix}\:\:&0&1&7&2&2\\ \:\:&0&5&7&4&0\\ \:\:&8&6&1&0&0\end{matrix}}\)
\(=93562\)
