Evaluate
\frac{43}{27}\approx 1.592592593
Factor
\frac{43}{3 ^ {3}} = 1\frac{16}{27} = 1.5925925925925926
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)43}\\\end{array}
Use the 1^{st} digit 4 from dividend 43
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)43}\\\end{array}
Since 4 is less than 27, use the next digit 3 from dividend 43 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)43}\\\end{array}
Use the 2^{nd} digit 3 from dividend 43
\begin{array}{l}\phantom{27)}01\phantom{4}\\27\overline{)43}\\\phantom{27)}\underline{\phantom{}27\phantom{}}\\\phantom{27)}16\\\end{array}
Find closest multiple of 27 to 43. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 43 to get reminder 16. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }16
Since 16 is less than 27, stop the division. The reminder is 16. 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}