Evaluate
\frac{23}{12}\approx 1.916666667
Factor
\frac{23}{2 ^ {2} \cdot 3} = 1\frac{11}{12} = 1.9166666666666667
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)23}\\\end{array}
Use the 1^{st} digit 2 from dividend 23
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)23}\\\end{array}
Since 2 is less than 12, use the next digit 3 from dividend 23 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)23}\\\end{array}
Use the 2^{nd} digit 3 from dividend 23
\begin{array}{l}\phantom{12)}01\phantom{4}\\12\overline{)23}\\\phantom{12)}\underline{\phantom{}12\phantom{}}\\\phantom{12)}11\\\end{array}
Find closest multiple of 12 to 23. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 23 to get reminder 11. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }11
Since 11 is less than 12, stop the division. The reminder is 11. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}