Evaluate
\frac{52}{25}=2.08
Factor
\frac{2 ^ {2} \cdot 13}{5 ^ {2}} = 2\frac{2}{25} = 2.08
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)208}\\\end{array}
Use the 1^{st} digit 2 from dividend 208
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)208}\\\end{array}
Since 2 is less than 100, use the next digit 0 from dividend 208 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)208}\\\end{array}
Use the 2^{nd} digit 0 from dividend 208
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)208}\\\end{array}
Since 20 is less than 100, use the next digit 8 from dividend 208 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)208}\\\end{array}
Use the 3^{rd} digit 8 from dividend 208
\begin{array}{l}\phantom{100)}002\phantom{6}\\100\overline{)208}\\\phantom{100)}\underline{\phantom{}200\phantom{}}\\\phantom{100)99}8\\\end{array}
Find closest multiple of 100 to 208. We see that 2 \times 100 = 200 is the nearest. Now subtract 200 from 208 to get reminder 8. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }8
Since 8 is less than 100, stop the division. The reminder is 8. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}