Evaluate
\frac{243}{20}=12.15
Factor
\frac{3 ^ {5}}{2 ^ {2} \cdot 5} = 12\frac{3}{20} = 12.15
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)1215}\\\end{array}
Use the 1^{st} digit 1 from dividend 1215
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)1215}\\\end{array}
Since 1 is less than 100, use the next digit 2 from dividend 1215 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)1215}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1215
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)1215}\\\end{array}
Since 12 is less than 100, use the next digit 1 from dividend 1215 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)1215}\\\end{array}
Use the 3^{rd} digit 1 from dividend 1215
\begin{array}{l}\phantom{100)}001\phantom{6}\\100\overline{)1215}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}21\\\end{array}
Find closest multiple of 100 to 121. We see that 1 \times 100 = 100 is the nearest. Now subtract 100 from 121 to get reminder 21. Add 1 to quotient.
\begin{array}{l}\phantom{100)}001\phantom{7}\\100\overline{)1215}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}215\\\end{array}
Use the 4^{th} digit 5 from dividend 1215
\begin{array}{l}\phantom{100)}0012\phantom{8}\\100\overline{)1215}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}215\\\phantom{100)}\underline{\phantom{9}200\phantom{}}\\\phantom{100)99}15\\\end{array}
Find closest multiple of 100 to 215. We see that 2 \times 100 = 200 is the nearest. Now subtract 200 from 215 to get reminder 15. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }15
Since 15 is less than 100, stop the division. The reminder is 15. The topmost line 0012 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}