Evaluate
\frac{360}{29}\approx 12.413793103
Factor
\frac{2 ^ {3} \cdot 3 ^ {2} \cdot 5}{29} = 12\frac{12}{29} = 12.413793103448276
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\begin{array}{l}\phantom{29)}\phantom{1}\\29\overline{)360}\\\end{array}
Use the 1^{st} digit 3 from dividend 360
\begin{array}{l}\phantom{29)}0\phantom{2}\\29\overline{)360}\\\end{array}
Since 3 is less than 29, use the next digit 6 from dividend 360 and add 0 to the quotient
\begin{array}{l}\phantom{29)}0\phantom{3}\\29\overline{)360}\\\end{array}
Use the 2^{nd} digit 6 from dividend 360
\begin{array}{l}\phantom{29)}01\phantom{4}\\29\overline{)360}\\\phantom{29)}\underline{\phantom{}29\phantom{9}}\\\phantom{29)9}7\\\end{array}
Find closest multiple of 29 to 36. We see that 1 \times 29 = 29 is the nearest. Now subtract 29 from 36 to get reminder 7. Add 1 to quotient.
\begin{array}{l}\phantom{29)}01\phantom{5}\\29\overline{)360}\\\phantom{29)}\underline{\phantom{}29\phantom{9}}\\\phantom{29)9}70\\\end{array}
Use the 3^{rd} digit 0 from dividend 360
\begin{array}{l}\phantom{29)}012\phantom{6}\\29\overline{)360}\\\phantom{29)}\underline{\phantom{}29\phantom{9}}\\\phantom{29)9}70\\\phantom{29)}\underline{\phantom{9}58\phantom{}}\\\phantom{29)9}12\\\end{array}
Find closest multiple of 29 to 70. We see that 2 \times 29 = 58 is the nearest. Now subtract 58 from 70 to get reminder 12. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }12
Since 12 is less than 29, stop the division. The reminder is 12. 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}