Evaluate
\frac{731}{60}\approx 12.183333333
Factor
\frac{17 \cdot 43}{2 ^ {2} \cdot 3 \cdot 5} = 12\frac{11}{60} = 12.183333333333334
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)731}\\\end{array}
Use the 1^{st} digit 7 from dividend 731
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)731}\\\end{array}
Since 7 is less than 60, use the next digit 3 from dividend 731 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)731}\\\end{array}
Use the 2^{nd} digit 3 from dividend 731
\begin{array}{l}\phantom{60)}01\phantom{4}\\60\overline{)731}\\\phantom{60)}\underline{\phantom{}60\phantom{9}}\\\phantom{60)}13\\\end{array}
Find closest multiple of 60 to 73. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 73 to get reminder 13. Add 1 to quotient.
\begin{array}{l}\phantom{60)}01\phantom{5}\\60\overline{)731}\\\phantom{60)}\underline{\phantom{}60\phantom{9}}\\\phantom{60)}131\\\end{array}
Use the 3^{rd} digit 1 from dividend 731
\begin{array}{l}\phantom{60)}012\phantom{6}\\60\overline{)731}\\\phantom{60)}\underline{\phantom{}60\phantom{9}}\\\phantom{60)}131\\\phantom{60)}\underline{\phantom{}120\phantom{}}\\\phantom{60)9}11\\\end{array}
Find closest multiple of 60 to 131. We see that 2 \times 60 = 120 is the nearest. Now subtract 120 from 131 to get reminder 11. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }11
Since 11 is less than 60, stop the division. The reminder is 11. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}