Evaluate
\frac{23}{3}\approx 7.666666667
Factor
\frac{23}{3} = 7\frac{2}{3} = 7.666666666666667
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)138}\\\end{array}
Use the 1^{st} digit 1 from dividend 138
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)138}\\\end{array}
Since 1 is less than 18, use the next digit 3 from dividend 138 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)138}\\\end{array}
Use the 2^{nd} digit 3 from dividend 138
\begin{array}{l}\phantom{18)}00\phantom{4}\\18\overline{)138}\\\end{array}
Since 13 is less than 18, use the next digit 8 from dividend 138 and add 0 to the quotient
\begin{array}{l}\phantom{18)}00\phantom{5}\\18\overline{)138}\\\end{array}
Use the 3^{rd} digit 8 from dividend 138
\begin{array}{l}\phantom{18)}007\phantom{6}\\18\overline{)138}\\\phantom{18)}\underline{\phantom{}126\phantom{}}\\\phantom{18)9}12\\\end{array}
Find closest multiple of 18 to 138. We see that 7 \times 18 = 126 is the nearest. Now subtract 126 from 138 to get reminder 12. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }12
Since 12 is less than 18, stop the division. The reminder is 12. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}