Evaluate
\frac{58}{15}\approx 3.866666667
Factor
\frac{2 \cdot 29}{3 \cdot 5} = 3\frac{13}{15} = 3.8666666666666667
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)232}\\\end{array}
Use the 1^{st} digit 2 from dividend 232
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)232}\\\end{array}
Since 2 is less than 60, use the next digit 3 from dividend 232 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)232}\\\end{array}
Use the 2^{nd} digit 3 from dividend 232
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)232}\\\end{array}
Since 23 is less than 60, use the next digit 2 from dividend 232 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)232}\\\end{array}
Use the 3^{rd} digit 2 from dividend 232
\begin{array}{l}\phantom{60)}003\phantom{6}\\60\overline{)232}\\\phantom{60)}\underline{\phantom{}180\phantom{}}\\\phantom{60)9}52\\\end{array}
Find closest multiple of 60 to 232. We see that 3 \times 60 = 180 is the nearest. Now subtract 180 from 232 to get reminder 52. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }52
Since 52 is less than 60, stop the division. The reminder is 52. 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}