Evaluate
\frac{281}{18}\approx 15.611111111
Factor
\frac{281}{2 \cdot 3 ^ {2}} = 15\frac{11}{18} = 15.61111111111111
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)843}\\\end{array}
Use the 1^{st} digit 8 from dividend 843
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)843}\\\end{array}
Since 8 is less than 54, use the next digit 4 from dividend 843 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)843}\\\end{array}
Use the 2^{nd} digit 4 from dividend 843
\begin{array}{l}\phantom{54)}01\phantom{4}\\54\overline{)843}\\\phantom{54)}\underline{\phantom{}54\phantom{9}}\\\phantom{54)}30\\\end{array}
Find closest multiple of 54 to 84. We see that 1 \times 54 = 54 is the nearest. Now subtract 54 from 84 to get reminder 30. Add 1 to quotient.
\begin{array}{l}\phantom{54)}01\phantom{5}\\54\overline{)843}\\\phantom{54)}\underline{\phantom{}54\phantom{9}}\\\phantom{54)}303\\\end{array}
Use the 3^{rd} digit 3 from dividend 843
\begin{array}{l}\phantom{54)}015\phantom{6}\\54\overline{)843}\\\phantom{54)}\underline{\phantom{}54\phantom{9}}\\\phantom{54)}303\\\phantom{54)}\underline{\phantom{}270\phantom{}}\\\phantom{54)9}33\\\end{array}
Find closest multiple of 54 to 303. We see that 5 \times 54 = 270 is the nearest. Now subtract 270 from 303 to get reminder 33. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }33
Since 33 is less than 54, stop the division. The reminder is 33. The topmost line 015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}