Evaluate
\frac{2192}{99}\approx 22.141414141
Factor
\frac{2 ^ {4} \cdot 137}{3 ^ {2} \cdot 11} = 22\frac{14}{99} = 22.141414141414142
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\begin{array}{l}\phantom{99)}\phantom{1}\\99\overline{)2192}\\\end{array}
Use the 1^{st} digit 2 from dividend 2192
\begin{array}{l}\phantom{99)}0\phantom{2}\\99\overline{)2192}\\\end{array}
Since 2 is less than 99, use the next digit 1 from dividend 2192 and add 0 to the quotient
\begin{array}{l}\phantom{99)}0\phantom{3}\\99\overline{)2192}\\\end{array}
Use the 2^{nd} digit 1 from dividend 2192
\begin{array}{l}\phantom{99)}00\phantom{4}\\99\overline{)2192}\\\end{array}
Since 21 is less than 99, use the next digit 9 from dividend 2192 and add 0 to the quotient
\begin{array}{l}\phantom{99)}00\phantom{5}\\99\overline{)2192}\\\end{array}
Use the 3^{rd} digit 9 from dividend 2192
\begin{array}{l}\phantom{99)}002\phantom{6}\\99\overline{)2192}\\\phantom{99)}\underline{\phantom{}198\phantom{9}}\\\phantom{99)9}21\\\end{array}
Find closest multiple of 99 to 219. We see that 2 \times 99 = 198 is the nearest. Now subtract 198 from 219 to get reminder 21. Add 2 to quotient.
\begin{array}{l}\phantom{99)}002\phantom{7}\\99\overline{)2192}\\\phantom{99)}\underline{\phantom{}198\phantom{9}}\\\phantom{99)9}212\\\end{array}
Use the 4^{th} digit 2 from dividend 2192
\begin{array}{l}\phantom{99)}0022\phantom{8}\\99\overline{)2192}\\\phantom{99)}\underline{\phantom{}198\phantom{9}}\\\phantom{99)9}212\\\phantom{99)}\underline{\phantom{9}198\phantom{}}\\\phantom{99)99}14\\\end{array}
Find closest multiple of 99 to 212. We see that 2 \times 99 = 198 is the nearest. Now subtract 198 from 212 to get reminder 14. Add 2 to quotient.
\text{Quotient: }22 \text{Reminder: }14
Since 14 is less than 99, stop the division. The reminder is 14. The topmost line 0022 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 22.
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}