Evaluate
\frac{43}{13}\approx 3.307692308
Factor
\frac{43}{13} = 3\frac{4}{13} = 3.3076923076923075
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\begin{array}{l}\phantom{650)}\phantom{1}\\650\overline{)2150}\\\end{array}
Use the 1^{st} digit 2 from dividend 2150
\begin{array}{l}\phantom{650)}0\phantom{2}\\650\overline{)2150}\\\end{array}
Since 2 is less than 650, use the next digit 1 from dividend 2150 and add 0 to the quotient
\begin{array}{l}\phantom{650)}0\phantom{3}\\650\overline{)2150}\\\end{array}
Use the 2^{nd} digit 1 from dividend 2150
\begin{array}{l}\phantom{650)}00\phantom{4}\\650\overline{)2150}\\\end{array}
Since 21 is less than 650, use the next digit 5 from dividend 2150 and add 0 to the quotient
\begin{array}{l}\phantom{650)}00\phantom{5}\\650\overline{)2150}\\\end{array}
Use the 3^{rd} digit 5 from dividend 2150
\begin{array}{l}\phantom{650)}000\phantom{6}\\650\overline{)2150}\\\end{array}
Since 215 is less than 650, use the next digit 0 from dividend 2150 and add 0 to the quotient
\begin{array}{l}\phantom{650)}000\phantom{7}\\650\overline{)2150}\\\end{array}
Use the 4^{th} digit 0 from dividend 2150
\begin{array}{l}\phantom{650)}0003\phantom{8}\\650\overline{)2150}\\\phantom{650)}\underline{\phantom{}1950\phantom{}}\\\phantom{650)9}200\\\end{array}
Find closest multiple of 650 to 2150. We see that 3 \times 650 = 1950 is the nearest. Now subtract 1950 from 2150 to get reminder 200. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }200
Since 200 is less than 650, stop the division. The reminder is 200. The topmost line 0003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}