Evaluate
\frac{25}{4}=6.25
Factor
\frac{5 ^ {2}}{2 ^ {2}} = 6\frac{1}{4} = 6.25
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)625}\\\end{array}
Use the 1^{st} digit 6 from dividend 625
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)625}\\\end{array}
Since 6 is less than 100, use the next digit 2 from dividend 625 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)625}\\\end{array}
Use the 2^{nd} digit 2 from dividend 625
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)625}\\\end{array}
Since 62 is less than 100, use the next digit 5 from dividend 625 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)625}\\\end{array}
Use the 3^{rd} digit 5 from dividend 625
\begin{array}{l}\phantom{100)}006\phantom{6}\\100\overline{)625}\\\phantom{100)}\underline{\phantom{}600\phantom{}}\\\phantom{100)9}25\\\end{array}
Find closest multiple of 100 to 625. We see that 6 \times 100 = 600 is the nearest. Now subtract 600 from 625 to get reminder 25. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }25
Since 25 is less than 100, stop the division. The reminder is 25. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}