Evaluate
\frac{230}{63}\approx 3.650793651
Factor
\frac{2 \cdot 5 \cdot 23}{3 ^ {2} \cdot 7} = 3\frac{41}{63} = 3.6507936507936507
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\begin{array}{l}\phantom{63)}\phantom{1}\\63\overline{)230}\\\end{array}
Use the 1^{st} digit 2 from dividend 230
\begin{array}{l}\phantom{63)}0\phantom{2}\\63\overline{)230}\\\end{array}
Since 2 is less than 63, use the next digit 3 from dividend 230 and add 0 to the quotient
\begin{array}{l}\phantom{63)}0\phantom{3}\\63\overline{)230}\\\end{array}
Use the 2^{nd} digit 3 from dividend 230
\begin{array}{l}\phantom{63)}00\phantom{4}\\63\overline{)230}\\\end{array}
Since 23 is less than 63, use the next digit 0 from dividend 230 and add 0 to the quotient
\begin{array}{l}\phantom{63)}00\phantom{5}\\63\overline{)230}\\\end{array}
Use the 3^{rd} digit 0 from dividend 230
\begin{array}{l}\phantom{63)}003\phantom{6}\\63\overline{)230}\\\phantom{63)}\underline{\phantom{}189\phantom{}}\\\phantom{63)9}41\\\end{array}
Find closest multiple of 63 to 230. We see that 3 \times 63 = 189 is the nearest. Now subtract 189 from 230 to get reminder 41. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }41
Since 41 is less than 63, stop the division. The reminder is 41. 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}