Evaluate
\frac{13}{5}=2.6
Factor
\frac{13}{5} = 2\frac{3}{5} = 2.6
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\begin{array}{l}\phantom{110)}\phantom{1}\\110\overline{)286}\\\end{array}
Use the 1^{st} digit 2 from dividend 286
\begin{array}{l}\phantom{110)}0\phantom{2}\\110\overline{)286}\\\end{array}
Since 2 is less than 110, use the next digit 8 from dividend 286 and add 0 to the quotient
\begin{array}{l}\phantom{110)}0\phantom{3}\\110\overline{)286}\\\end{array}
Use the 2^{nd} digit 8 from dividend 286
\begin{array}{l}\phantom{110)}00\phantom{4}\\110\overline{)286}\\\end{array}
Since 28 is less than 110, use the next digit 6 from dividend 286 and add 0 to the quotient
\begin{array}{l}\phantom{110)}00\phantom{5}\\110\overline{)286}\\\end{array}
Use the 3^{rd} digit 6 from dividend 286
\begin{array}{l}\phantom{110)}002\phantom{6}\\110\overline{)286}\\\phantom{110)}\underline{\phantom{}220\phantom{}}\\\phantom{110)9}66\\\end{array}
Find closest multiple of 110 to 286. We see that 2 \times 110 = 220 is the nearest. Now subtract 220 from 286 to get reminder 66. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }66
Since 66 is less than 110, stop the division. The reminder is 66. 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}