Evaluate
\frac{23}{13}\approx 1.769230769
Factor
\frac{23}{13} = 1\frac{10}{13} = 1.7692307692307692
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)23}\\\end{array}
Use the 1^{st} digit 2 from dividend 23
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)23}\\\end{array}
Since 2 is less than 13, use the next digit 3 from dividend 23 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)23}\\\end{array}
Use the 2^{nd} digit 3 from dividend 23
\begin{array}{l}\phantom{13)}01\phantom{4}\\13\overline{)23}\\\phantom{13)}\underline{\phantom{}13\phantom{}}\\\phantom{13)}10\\\end{array}
Find closest multiple of 13 to 23. We see that 1 \times 13 = 13 is the nearest. Now subtract 13 from 23 to get reminder 10. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }10
Since 10 is less than 13, stop the division. The reminder is 10. 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}