Evaluate
\frac{263}{23}\approx 11.434782609
Factor
\frac{263}{23} = 11\frac{10}{23} = 11.434782608695652
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\begin{array}{l}\phantom{69)}\phantom{1}\\69\overline{)789}\\\end{array}
Use the 1^{st} digit 7 from dividend 789
\begin{array}{l}\phantom{69)}0\phantom{2}\\69\overline{)789}\\\end{array}
Since 7 is less than 69, use the next digit 8 from dividend 789 and add 0 to the quotient
\begin{array}{l}\phantom{69)}0\phantom{3}\\69\overline{)789}\\\end{array}
Use the 2^{nd} digit 8 from dividend 789
\begin{array}{l}\phantom{69)}01\phantom{4}\\69\overline{)789}\\\phantom{69)}\underline{\phantom{}69\phantom{9}}\\\phantom{69)9}9\\\end{array}
Find closest multiple of 69 to 78. We see that 1 \times 69 = 69 is the nearest. Now subtract 69 from 78 to get reminder 9. Add 1 to quotient.
\begin{array}{l}\phantom{69)}01\phantom{5}\\69\overline{)789}\\\phantom{69)}\underline{\phantom{}69\phantom{9}}\\\phantom{69)9}99\\\end{array}
Use the 3^{rd} digit 9 from dividend 789
\begin{array}{l}\phantom{69)}011\phantom{6}\\69\overline{)789}\\\phantom{69)}\underline{\phantom{}69\phantom{9}}\\\phantom{69)9}99\\\phantom{69)}\underline{\phantom{9}69\phantom{}}\\\phantom{69)9}30\\\end{array}
Find closest multiple of 69 to 99. We see that 1 \times 69 = 69 is the nearest. Now subtract 69 from 99 to get reminder 30. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }30
Since 30 is less than 69, stop the division. The reminder is 30. The topmost line 011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.
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}