Evaluate
\frac{99955}{3}\approx 33318.333333333
Factor
\frac{5 \cdot 19991}{3} = 33318\frac{1}{3} = 33318.333333333336
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)399820}\\\end{array}
Use the 1^{st} digit 3 from dividend 399820
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)399820}\\\end{array}
Since 3 is less than 12, use the next digit 9 from dividend 399820 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)399820}\\\end{array}
Use the 2^{nd} digit 9 from dividend 399820
\begin{array}{l}\phantom{12)}03\phantom{4}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}3\\\end{array}
Find closest multiple of 12 to 39. We see that 3 \times 12 = 36 is the nearest. Now subtract 36 from 39 to get reminder 3. Add 3 to quotient.
\begin{array}{l}\phantom{12)}03\phantom{5}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}39\\\end{array}
Use the 3^{rd} digit 9 from dividend 399820
\begin{array}{l}\phantom{12)}033\phantom{6}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}39\\\phantom{12)}\underline{\phantom{9}36\phantom{999}}\\\phantom{12)99}3\\\end{array}
Find closest multiple of 12 to 39. We see that 3 \times 12 = 36 is the nearest. Now subtract 36 from 39 to get reminder 3. Add 3 to quotient.
\begin{array}{l}\phantom{12)}033\phantom{7}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}39\\\phantom{12)}\underline{\phantom{9}36\phantom{999}}\\\phantom{12)99}38\\\end{array}
Use the 4^{th} digit 8 from dividend 399820
\begin{array}{l}\phantom{12)}0333\phantom{8}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}39\\\phantom{12)}\underline{\phantom{9}36\phantom{999}}\\\phantom{12)99}38\\\phantom{12)}\underline{\phantom{99}36\phantom{99}}\\\phantom{12)999}2\\\end{array}
Find closest multiple of 12 to 38. We see that 3 \times 12 = 36 is the nearest. Now subtract 36 from 38 to get reminder 2. Add 3 to quotient.
\begin{array}{l}\phantom{12)}0333\phantom{9}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}39\\\phantom{12)}\underline{\phantom{9}36\phantom{999}}\\\phantom{12)99}38\\\phantom{12)}\underline{\phantom{99}36\phantom{99}}\\\phantom{12)999}22\\\end{array}
Use the 5^{th} digit 2 from dividend 399820
\begin{array}{l}\phantom{12)}03331\phantom{10}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}39\\\phantom{12)}\underline{\phantom{9}36\phantom{999}}\\\phantom{12)99}38\\\phantom{12)}\underline{\phantom{99}36\phantom{99}}\\\phantom{12)999}22\\\phantom{12)}\underline{\phantom{999}12\phantom{9}}\\\phantom{12)999}10\\\end{array}
Find closest multiple of 12 to 22. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 22 to get reminder 10. Add 1 to quotient.
\begin{array}{l}\phantom{12)}03331\phantom{11}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}39\\\phantom{12)}\underline{\phantom{9}36\phantom{999}}\\\phantom{12)99}38\\\phantom{12)}\underline{\phantom{99}36\phantom{99}}\\\phantom{12)999}22\\\phantom{12)}\underline{\phantom{999}12\phantom{9}}\\\phantom{12)999}100\\\end{array}
Use the 6^{th} digit 0 from dividend 399820
\begin{array}{l}\phantom{12)}033318\phantom{12}\\12\overline{)399820}\\\phantom{12)}\underline{\phantom{}36\phantom{9999}}\\\phantom{12)9}39\\\phantom{12)}\underline{\phantom{9}36\phantom{999}}\\\phantom{12)99}38\\\phantom{12)}\underline{\phantom{99}36\phantom{99}}\\\phantom{12)999}22\\\phantom{12)}\underline{\phantom{999}12\phantom{9}}\\\phantom{12)999}100\\\phantom{12)}\underline{\phantom{9999}96\phantom{}}\\\phantom{12)99999}4\\\end{array}
Find closest multiple of 12 to 100. We see that 8 \times 12 = 96 is the nearest. Now subtract 96 from 100 to get reminder 4. Add 8 to quotient.
\text{Quotient: }33318 \text{Reminder: }4
Since 4 is less than 12, stop the division. The reminder is 4. The topmost line 033318 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 33318.
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}