+0

question

0
233
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what is 287 * 326
Jun 16, 2022

#1
+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
+514
+3

$$287\cdot \:326=93562$$

$$Line\:up\:the\:numbers$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$=93562$$

mworkhard222 Jun 16, 2022
#2
+118607
+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