Evaluate
\frac{28263}{125}=226.104
Factor
\frac{3 \cdot 9421}{5 ^ {3}} = 226\frac{13}{125} = 226.104
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\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)226104}\\\end{array}
Use the 1^{st} digit 2 from dividend 226104
\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)226104}\\\end{array}
Since 2 is less than 1000, use the next digit 2 from dividend 226104 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)226104}\\\end{array}
Use the 2^{nd} digit 2 from dividend 226104
\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)226104}\\\end{array}
Since 22 is less than 1000, use the next digit 6 from dividend 226104 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)226104}\\\end{array}
Use the 3^{rd} digit 6 from dividend 226104
\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)226104}\\\end{array}
Since 226 is less than 1000, use the next digit 1 from dividend 226104 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)226104}\\\end{array}
Use the 4^{th} digit 1 from dividend 226104
\begin{array}{l}\phantom{1000)}0002\phantom{8}\\1000\overline{)226104}\\\phantom{1000)}\underline{\phantom{}2000\phantom{99}}\\\phantom{1000)9}261\\\end{array}
Find closest multiple of 1000 to 2261. We see that 2 \times 1000 = 2000 is the nearest. Now subtract 2000 from 2261 to get reminder 261. Add 2 to quotient.
\begin{array}{l}\phantom{1000)}0002\phantom{9}\\1000\overline{)226104}\\\phantom{1000)}\underline{\phantom{}2000\phantom{99}}\\\phantom{1000)9}2610\\\end{array}
Use the 5^{th} digit 0 from dividend 226104
\begin{array}{l}\phantom{1000)}00022\phantom{10}\\1000\overline{)226104}\\\phantom{1000)}\underline{\phantom{}2000\phantom{99}}\\\phantom{1000)9}2610\\\phantom{1000)}\underline{\phantom{9}2000\phantom{9}}\\\phantom{1000)99}610\\\end{array}
Find closest multiple of 1000 to 2610. We see that 2 \times 1000 = 2000 is the nearest. Now subtract 2000 from 2610 to get reminder 610. Add 2 to quotient.
\begin{array}{l}\phantom{1000)}00022\phantom{11}\\1000\overline{)226104}\\\phantom{1000)}\underline{\phantom{}2000\phantom{99}}\\\phantom{1000)9}2610\\\phantom{1000)}\underline{\phantom{9}2000\phantom{9}}\\\phantom{1000)99}6104\\\end{array}
Use the 6^{th} digit 4 from dividend 226104
\begin{array}{l}\phantom{1000)}000226\phantom{12}\\1000\overline{)226104}\\\phantom{1000)}\underline{\phantom{}2000\phantom{99}}\\\phantom{1000)9}2610\\\phantom{1000)}\underline{\phantom{9}2000\phantom{9}}\\\phantom{1000)99}6104\\\phantom{1000)}\underline{\phantom{99}6000\phantom{}}\\\phantom{1000)999}104\\\end{array}
Find closest multiple of 1000 to 6104. We see that 6 \times 1000 = 6000 is the nearest. Now subtract 6000 from 6104 to get reminder 104. Add 6 to quotient.
\text{Quotient: }226 \text{Reminder: }104
Since 104 is less than 1000, stop the division. The reminder is 104. The topmost line 000226 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 226.
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}