Evaluate
\frac{13}{5}=2.6
Factor
\frac{13}{5} = 2\frac{3}{5} = 2.6
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)65}\\\end{array}
Use the 1^{st} digit 6 from dividend 65
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)65}\\\end{array}
Since 6 is less than 25, use the next digit 5 from dividend 65 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)65}\\\end{array}
Use the 2^{nd} digit 5 from dividend 65
\begin{array}{l}\phantom{25)}02\phantom{4}\\25\overline{)65}\\\phantom{25)}\underline{\phantom{}50\phantom{}}\\\phantom{25)}15\\\end{array}
Find closest multiple of 25 to 65. We see that 2 \times 25 = 50 is the nearest. Now subtract 50 from 65 to get reminder 15. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }15
Since 15 is less than 25, stop the division. The reminder is 15. The topmost line 02 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}