Evaluate
\frac{108}{23}\approx 4.695652174
Factor
\frac{2 ^ {2} \cdot 3 ^ {3}}{23} = 4\frac{16}{23} = 4.695652173913044
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)108}\\\end{array}
Use the 1^{st} digit 1 from dividend 108
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)108}\\\end{array}
Since 1 is less than 23, use the next digit 0 from dividend 108 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)108}\\\end{array}
Use the 2^{nd} digit 0 from dividend 108
\begin{array}{l}\phantom{23)}00\phantom{4}\\23\overline{)108}\\\end{array}
Since 10 is less than 23, use the next digit 8 from dividend 108 and add 0 to the quotient
\begin{array}{l}\phantom{23)}00\phantom{5}\\23\overline{)108}\\\end{array}
Use the 3^{rd} digit 8 from dividend 108
\begin{array}{l}\phantom{23)}004\phantom{6}\\23\overline{)108}\\\phantom{23)}\underline{\phantom{9}92\phantom{}}\\\phantom{23)9}16\\\end{array}
Find closest multiple of 23 to 108. We see that 4 \times 23 = 92 is the nearest. Now subtract 92 from 108 to get reminder 16. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }16
Since 16 is less than 23, stop the division. The reminder is 16. 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}