Evaluate
\frac{7}{2}=3.5
Factor
\frac{7}{2} = 3\frac{1}{2} = 3.5
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)189}\\\end{array}
Use the 1^{st} digit 1 from dividend 189
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)189}\\\end{array}
Since 1 is less than 54, use the next digit 8 from dividend 189 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)189}\\\end{array}
Use the 2^{nd} digit 8 from dividend 189
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)189}\\\end{array}
Since 18 is less than 54, use the next digit 9 from dividend 189 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)189}\\\end{array}
Use the 3^{rd} digit 9 from dividend 189
\begin{array}{l}\phantom{54)}003\phantom{6}\\54\overline{)189}\\\phantom{54)}\underline{\phantom{}162\phantom{}}\\\phantom{54)9}27\\\end{array}
Find closest multiple of 54 to 189. We see that 3 \times 54 = 162 is the nearest. Now subtract 162 from 189 to get reminder 27. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }27
Since 27 is less than 54, stop the division. The reminder is 27. The topmost line 003 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}