Evaluate
\frac{27}{16}=1.6875
Factor
\frac{3 ^ {3}}{2 ^ {4}} = 1\frac{11}{16} = 1.6875
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\begin{array}{l}\phantom{32)}\phantom{1}\\32\overline{)54}\\\end{array}
Use the 1^{st} digit 5 from dividend 54
\begin{array}{l}\phantom{32)}0\phantom{2}\\32\overline{)54}\\\end{array}
Since 5 is less than 32, use the next digit 4 from dividend 54 and add 0 to the quotient
\begin{array}{l}\phantom{32)}0\phantom{3}\\32\overline{)54}\\\end{array}
Use the 2^{nd} digit 4 from dividend 54
\begin{array}{l}\phantom{32)}01\phantom{4}\\32\overline{)54}\\\phantom{32)}\underline{\phantom{}32\phantom{}}\\\phantom{32)}22\\\end{array}
Find closest multiple of 32 to 54. We see that 1 \times 32 = 32 is the nearest. Now subtract 32 from 54 to get reminder 22. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }22
Since 22 is less than 32, stop the division. The reminder is 22. 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}