Evaluate
\frac{25000}{11}\approx 2272.727272727
Factor
\frac{2 ^ {3} \cdot 5 ^ {5}}{11} = 2272\frac{8}{11} = 2272.7272727272725
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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)125000}\\\end{array}
Use the 1^{st} digit 1 from dividend 125000
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)125000}\\\end{array}
Since 1 is less than 55, use the next digit 2 from dividend 125000 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)125000}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125000
\begin{array}{l}\phantom{55)}00\phantom{4}\\55\overline{)125000}\\\end{array}
Since 12 is less than 55, use the next digit 5 from dividend 125000 and add 0 to the quotient
\begin{array}{l}\phantom{55)}00\phantom{5}\\55\overline{)125000}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125000
\begin{array}{l}\phantom{55)}002\phantom{6}\\55\overline{)125000}\\\phantom{55)}\underline{\phantom{}110\phantom{999}}\\\phantom{55)9}15\\\end{array}
Find closest multiple of 55 to 125. We see that 2 \times 55 = 110 is the nearest. Now subtract 110 from 125 to get reminder 15. Add 2 to quotient.
\begin{array}{l}\phantom{55)}002\phantom{7}\\55\overline{)125000}\\\phantom{55)}\underline{\phantom{}110\phantom{999}}\\\phantom{55)9}150\\\end{array}
Use the 4^{th} digit 0 from dividend 125000
\begin{array}{l}\phantom{55)}0022\phantom{8}\\55\overline{)125000}\\\phantom{55)}\underline{\phantom{}110\phantom{999}}\\\phantom{55)9}150\\\phantom{55)}\underline{\phantom{9}110\phantom{99}}\\\phantom{55)99}40\\\end{array}
Find closest multiple of 55 to 150. We see that 2 \times 55 = 110 is the nearest. Now subtract 110 from 150 to get reminder 40. Add 2 to quotient.
\begin{array}{l}\phantom{55)}0022\phantom{9}\\55\overline{)125000}\\\phantom{55)}\underline{\phantom{}110\phantom{999}}\\\phantom{55)9}150\\\phantom{55)}\underline{\phantom{9}110\phantom{99}}\\\phantom{55)99}400\\\end{array}
Use the 5^{th} digit 0 from dividend 125000
\begin{array}{l}\phantom{55)}00227\phantom{10}\\55\overline{)125000}\\\phantom{55)}\underline{\phantom{}110\phantom{999}}\\\phantom{55)9}150\\\phantom{55)}\underline{\phantom{9}110\phantom{99}}\\\phantom{55)99}400\\\phantom{55)}\underline{\phantom{99}385\phantom{9}}\\\phantom{55)999}15\\\end{array}
Find closest multiple of 55 to 400. We see that 7 \times 55 = 385 is the nearest. Now subtract 385 from 400 to get reminder 15. Add 7 to quotient.
\begin{array}{l}\phantom{55)}00227\phantom{11}\\55\overline{)125000}\\\phantom{55)}\underline{\phantom{}110\phantom{999}}\\\phantom{55)9}150\\\phantom{55)}\underline{\phantom{9}110\phantom{99}}\\\phantom{55)99}400\\\phantom{55)}\underline{\phantom{99}385\phantom{9}}\\\phantom{55)999}150\\\end{array}
Use the 6^{th} digit 0 from dividend 125000
\begin{array}{l}\phantom{55)}002272\phantom{12}\\55\overline{)125000}\\\phantom{55)}\underline{\phantom{}110\phantom{999}}\\\phantom{55)9}150\\\phantom{55)}\underline{\phantom{9}110\phantom{99}}\\\phantom{55)99}400\\\phantom{55)}\underline{\phantom{99}385\phantom{9}}\\\phantom{55)999}150\\\phantom{55)}\underline{\phantom{999}110\phantom{}}\\\phantom{55)9999}40\\\end{array}
Find closest multiple of 55 to 150. We see that 2 \times 55 = 110 is the nearest. Now subtract 110 from 150 to get reminder 40. Add 2 to quotient.
\text{Quotient: }2272 \text{Reminder: }40
Since 40 is less than 55, stop the division. The reminder is 40. The topmost line 002272 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2272.
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}