Evaluate
\frac{31}{12}\approx 2.583333333
Factor
\frac{31}{2 ^ {2} \cdot 3} = 2\frac{7}{12} = 2.5833333333333335
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)155}\\\end{array}
Use the 1^{st} digit 1 from dividend 155
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)155}\\\end{array}
Since 1 is less than 60, use the next digit 5 from dividend 155 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)155}\\\end{array}
Use the 2^{nd} digit 5 from dividend 155
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)155}\\\end{array}
Since 15 is less than 60, use the next digit 5 from dividend 155 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)155}\\\end{array}
Use the 3^{rd} digit 5 from dividend 155
\begin{array}{l}\phantom{60)}002\phantom{6}\\60\overline{)155}\\\phantom{60)}\underline{\phantom{}120\phantom{}}\\\phantom{60)9}35\\\end{array}
Find closest multiple of 60 to 155. We see that 2 \times 60 = 120 is the nearest. Now subtract 120 from 155 to get reminder 35. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }35
Since 35 is less than 60, stop the division. The reminder is 35. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}