Evaluate
\frac{43}{23}\approx 1.869565217
Factor
\frac{43}{23} = 1\frac{20}{23} = 1.8695652173913044
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\begin{array}{l}\phantom{46)}\phantom{1}\\46\overline{)86}\\\end{array}
Use the 1^{st} digit 8 from dividend 86
\begin{array}{l}\phantom{46)}0\phantom{2}\\46\overline{)86}\\\end{array}
Since 8 is less than 46, use the next digit 6 from dividend 86 and add 0 to the quotient
\begin{array}{l}\phantom{46)}0\phantom{3}\\46\overline{)86}\\\end{array}
Use the 2^{nd} digit 6 from dividend 86
\begin{array}{l}\phantom{46)}01\phantom{4}\\46\overline{)86}\\\phantom{46)}\underline{\phantom{}46\phantom{}}\\\phantom{46)}40\\\end{array}
Find closest multiple of 46 to 86. We see that 1 \times 46 = 46 is the nearest. Now subtract 46 from 86 to get reminder 40. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }40
Since 40 is less than 46, stop the division. The reminder is 40. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}