Evaluate
\frac{11000}{3}\approx 3666.666666667
Factor
\frac{2 ^ {3} \cdot 5 ^ {3} \cdot 11}{3} = 3666\frac{2}{3} = 3666.6666666666665
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)55000}\\\end{array}
Use the 1^{st} digit 5 from dividend 55000
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)55000}\\\end{array}
Since 5 is less than 15, use the next digit 5 from dividend 55000 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)55000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 55000
\begin{array}{l}\phantom{15)}03\phantom{4}\\15\overline{)55000}\\\phantom{15)}\underline{\phantom{}45\phantom{999}}\\\phantom{15)}10\\\end{array}
Find closest multiple of 15 to 55. We see that 3 \times 15 = 45 is the nearest. Now subtract 45 from 55 to get reminder 10. Add 3 to quotient.
\begin{array}{l}\phantom{15)}03\phantom{5}\\15\overline{)55000}\\\phantom{15)}\underline{\phantom{}45\phantom{999}}\\\phantom{15)}100\\\end{array}
Use the 3^{rd} digit 0 from dividend 55000
\begin{array}{l}\phantom{15)}036\phantom{6}\\15\overline{)55000}\\\phantom{15)}\underline{\phantom{}45\phantom{999}}\\\phantom{15)}100\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)9}10\\\end{array}
Find closest multiple of 15 to 100. We see that 6 \times 15 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 6 to quotient.
\begin{array}{l}\phantom{15)}036\phantom{7}\\15\overline{)55000}\\\phantom{15)}\underline{\phantom{}45\phantom{999}}\\\phantom{15)}100\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 55000
\begin{array}{l}\phantom{15)}0366\phantom{8}\\15\overline{)55000}\\\phantom{15)}\underline{\phantom{}45\phantom{999}}\\\phantom{15)}100\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)9}100\\\phantom{15)}\underline{\phantom{99}90\phantom{9}}\\\phantom{15)99}10\\\end{array}
Find closest multiple of 15 to 100. We see that 6 \times 15 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 6 to quotient.
\begin{array}{l}\phantom{15)}0366\phantom{9}\\15\overline{)55000}\\\phantom{15)}\underline{\phantom{}45\phantom{999}}\\\phantom{15)}100\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)9}100\\\phantom{15)}\underline{\phantom{99}90\phantom{9}}\\\phantom{15)99}100\\\end{array}
Use the 5^{th} digit 0 from dividend 55000
\begin{array}{l}\phantom{15)}03666\phantom{10}\\15\overline{)55000}\\\phantom{15)}\underline{\phantom{}45\phantom{999}}\\\phantom{15)}100\\\phantom{15)}\underline{\phantom{9}90\phantom{99}}\\\phantom{15)9}100\\\phantom{15)}\underline{\phantom{99}90\phantom{9}}\\\phantom{15)99}100\\\phantom{15)}\underline{\phantom{999}90\phantom{}}\\\phantom{15)999}10\\\end{array}
Find closest multiple of 15 to 100. We see that 6 \times 15 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 6 to quotient.
\text{Quotient: }3666 \text{Reminder: }10
Since 10 is less than 15, stop the division. The reminder is 10. The topmost line 03666 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3666.
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}