Evaluate
\frac{209}{15}\approx 13.933333333
Factor
\frac{11 \cdot 19}{3 \cdot 5} = 13\frac{14}{15} = 13.933333333333334
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)418}\\\end{array}
Use the 1^{st} digit 4 from dividend 418
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)418}\\\end{array}
Since 4 is less than 30, use the next digit 1 from dividend 418 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)418}\\\end{array}
Use the 2^{nd} digit 1 from dividend 418
\begin{array}{l}\phantom{30)}01\phantom{4}\\30\overline{)418}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}11\\\end{array}
Find closest multiple of 30 to 41. We see that 1 \times 30 = 30 is the nearest. Now subtract 30 from 41 to get reminder 11. Add 1 to quotient.
\begin{array}{l}\phantom{30)}01\phantom{5}\\30\overline{)418}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}118\\\end{array}
Use the 3^{rd} digit 8 from dividend 418
\begin{array}{l}\phantom{30)}013\phantom{6}\\30\overline{)418}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}118\\\phantom{30)}\underline{\phantom{9}90\phantom{}}\\\phantom{30)9}28\\\end{array}
Find closest multiple of 30 to 118. We see that 3 \times 30 = 90 is the nearest. Now subtract 90 from 118 to get reminder 28. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }28
Since 28 is less than 30, stop the division. The reminder is 28. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}