Evaluate
\frac{9}{2}=4.5
Factor
\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)189}\\\end{array}
Use the 1^{st} digit 1 from dividend 189
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)189}\\\end{array}
Since 1 is less than 42, use the next digit 8 from dividend 189 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)189}\\\end{array}
Use the 2^{nd} digit 8 from dividend 189
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)189}\\\end{array}
Since 18 is less than 42, use the next digit 9 from dividend 189 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)189}\\\end{array}
Use the 3^{rd} digit 9 from dividend 189
\begin{array}{l}\phantom{42)}004\phantom{6}\\42\overline{)189}\\\phantom{42)}\underline{\phantom{}168\phantom{}}\\\phantom{42)9}21\\\end{array}
Find closest multiple of 42 to 189. We see that 4 \times 42 = 168 is the nearest. Now subtract 168 from 189 to get reminder 21. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }21
Since 21 is less than 42, stop the division. The reminder is 21. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}