Evaluate
\frac{537}{13}\approx 41.307692308
Factor
\frac{3 \cdot 179}{13} = 41\frac{4}{13} = 41.30769230769231
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)537}\\\end{array}
Use the 1^{st} digit 5 from dividend 537
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)537}\\\end{array}
Since 5 is less than 13, use the next digit 3 from dividend 537 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)537}\\\end{array}
Use the 2^{nd} digit 3 from dividend 537
\begin{array}{l}\phantom{13)}04\phantom{4}\\13\overline{)537}\\\phantom{13)}\underline{\phantom{}52\phantom{9}}\\\phantom{13)9}1\\\end{array}
Find closest multiple of 13 to 53. We see that 4 \times 13 = 52 is the nearest. Now subtract 52 from 53 to get reminder 1. Add 4 to quotient.
\begin{array}{l}\phantom{13)}04\phantom{5}\\13\overline{)537}\\\phantom{13)}\underline{\phantom{}52\phantom{9}}\\\phantom{13)9}17\\\end{array}
Use the 3^{rd} digit 7 from dividend 537
\begin{array}{l}\phantom{13)}041\phantom{6}\\13\overline{)537}\\\phantom{13)}\underline{\phantom{}52\phantom{9}}\\\phantom{13)9}17\\\phantom{13)}\underline{\phantom{9}13\phantom{}}\\\phantom{13)99}4\\\end{array}
Find closest multiple of 13 to 17. We see that 1 \times 13 = 13 is the nearest. Now subtract 13 from 17 to get reminder 4. Add 1 to quotient.
\text{Quotient: }41 \text{Reminder: }4
Since 4 is less than 13, stop the division. The reminder is 4. The topmost line 041 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 41.
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}