Evaluate
\frac{25}{2}=12.5
Factor
\frac{5 ^ {2}}{2} = 12\frac{1}{2} = 12.5
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\begin{array}{l}\phantom{168)}\phantom{1}\\168\overline{)2100}\\\end{array}
Use the 1^{st} digit 2 from dividend 2100
\begin{array}{l}\phantom{168)}0\phantom{2}\\168\overline{)2100}\\\end{array}
Since 2 is less than 168, use the next digit 1 from dividend 2100 and add 0 to the quotient
\begin{array}{l}\phantom{168)}0\phantom{3}\\168\overline{)2100}\\\end{array}
Use the 2^{nd} digit 1 from dividend 2100
\begin{array}{l}\phantom{168)}00\phantom{4}\\168\overline{)2100}\\\end{array}
Since 21 is less than 168, use the next digit 0 from dividend 2100 and add 0 to the quotient
\begin{array}{l}\phantom{168)}00\phantom{5}\\168\overline{)2100}\\\end{array}
Use the 3^{rd} digit 0 from dividend 2100
\begin{array}{l}\phantom{168)}001\phantom{6}\\168\overline{)2100}\\\phantom{168)}\underline{\phantom{}168\phantom{9}}\\\phantom{168)9}42\\\end{array}
Find closest multiple of 168 to 210. We see that 1 \times 168 = 168 is the nearest. Now subtract 168 from 210 to get reminder 42. Add 1 to quotient.
\begin{array}{l}\phantom{168)}001\phantom{7}\\168\overline{)2100}\\\phantom{168)}\underline{\phantom{}168\phantom{9}}\\\phantom{168)9}420\\\end{array}
Use the 4^{th} digit 0 from dividend 2100
\begin{array}{l}\phantom{168)}0012\phantom{8}\\168\overline{)2100}\\\phantom{168)}\underline{\phantom{}168\phantom{9}}\\\phantom{168)9}420\\\phantom{168)}\underline{\phantom{9}336\phantom{}}\\\phantom{168)99}84\\\end{array}
Find closest multiple of 168 to 420. We see that 2 \times 168 = 336 is the nearest. Now subtract 336 from 420 to get reminder 84. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }84
Since 84 is less than 168, stop the division. The reminder is 84. 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}