Evaluate
\frac{7809}{23}\approx 339.52173913
Factor
\frac{3 \cdot 19 \cdot 137}{23} = 339\frac{12}{23} = 339.5217391304348
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)7809}\\\end{array}
Use the 1^{st} digit 7 from dividend 7809
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)7809}\\\end{array}
Since 7 is less than 23, use the next digit 8 from dividend 7809 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)7809}\\\end{array}
Use the 2^{nd} digit 8 from dividend 7809
\begin{array}{l}\phantom{23)}03\phantom{4}\\23\overline{)7809}\\\phantom{23)}\underline{\phantom{}69\phantom{99}}\\\phantom{23)9}9\\\end{array}
Find closest multiple of 23 to 78. We see that 3 \times 23 = 69 is the nearest. Now subtract 69 from 78 to get reminder 9. Add 3 to quotient.
\begin{array}{l}\phantom{23)}03\phantom{5}\\23\overline{)7809}\\\phantom{23)}\underline{\phantom{}69\phantom{99}}\\\phantom{23)9}90\\\end{array}
Use the 3^{rd} digit 0 from dividend 7809
\begin{array}{l}\phantom{23)}033\phantom{6}\\23\overline{)7809}\\\phantom{23)}\underline{\phantom{}69\phantom{99}}\\\phantom{23)9}90\\\phantom{23)}\underline{\phantom{9}69\phantom{9}}\\\phantom{23)9}21\\\end{array}
Find closest multiple of 23 to 90. We see that 3 \times 23 = 69 is the nearest. Now subtract 69 from 90 to get reminder 21. Add 3 to quotient.
\begin{array}{l}\phantom{23)}033\phantom{7}\\23\overline{)7809}\\\phantom{23)}\underline{\phantom{}69\phantom{99}}\\\phantom{23)9}90\\\phantom{23)}\underline{\phantom{9}69\phantom{9}}\\\phantom{23)9}219\\\end{array}
Use the 4^{th} digit 9 from dividend 7809
\begin{array}{l}\phantom{23)}0339\phantom{8}\\23\overline{)7809}\\\phantom{23)}\underline{\phantom{}69\phantom{99}}\\\phantom{23)9}90\\\phantom{23)}\underline{\phantom{9}69\phantom{9}}\\\phantom{23)9}219\\\phantom{23)}\underline{\phantom{9}207\phantom{}}\\\phantom{23)99}12\\\end{array}
Find closest multiple of 23 to 219. We see that 9 \times 23 = 207 is the nearest. Now subtract 207 from 219 to get reminder 12. Add 9 to quotient.
\text{Quotient: }339 \text{Reminder: }12
Since 12 is less than 23, stop the division. The reminder is 12. The topmost line 0339 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 339.
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}