Evaluate
\frac{11111}{445}\approx 24.968539326
Factor
\frac{41 \cdot 271}{5 \cdot 89} = 24\frac{431}{445} = 24.968539325842695
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\begin{array}{l}\phantom{2225)}\phantom{1}\\2225\overline{)55555}\\\end{array}
Use the 1^{st} digit 5 from dividend 55555
\begin{array}{l}\phantom{2225)}0\phantom{2}\\2225\overline{)55555}\\\end{array}
Since 5 is less than 2225, use the next digit 5 from dividend 55555 and add 0 to the quotient
\begin{array}{l}\phantom{2225)}0\phantom{3}\\2225\overline{)55555}\\\end{array}
Use the 2^{nd} digit 5 from dividend 55555
\begin{array}{l}\phantom{2225)}00\phantom{4}\\2225\overline{)55555}\\\end{array}
Since 55 is less than 2225, use the next digit 5 from dividend 55555 and add 0 to the quotient
\begin{array}{l}\phantom{2225)}00\phantom{5}\\2225\overline{)55555}\\\end{array}
Use the 3^{rd} digit 5 from dividend 55555
\begin{array}{l}\phantom{2225)}000\phantom{6}\\2225\overline{)55555}\\\end{array}
Since 555 is less than 2225, use the next digit 5 from dividend 55555 and add 0 to the quotient
\begin{array}{l}\phantom{2225)}000\phantom{7}\\2225\overline{)55555}\\\end{array}
Use the 4^{th} digit 5 from dividend 55555
\begin{array}{l}\phantom{2225)}0002\phantom{8}\\2225\overline{)55555}\\\phantom{2225)}\underline{\phantom{}4450\phantom{9}}\\\phantom{2225)}1105\\\end{array}
Find closest multiple of 2225 to 5555. We see that 2 \times 2225 = 4450 is the nearest. Now subtract 4450 from 5555 to get reminder 1105. Add 2 to quotient.
\begin{array}{l}\phantom{2225)}0002\phantom{9}\\2225\overline{)55555}\\\phantom{2225)}\underline{\phantom{}4450\phantom{9}}\\\phantom{2225)}11055\\\end{array}
Use the 5^{th} digit 5 from dividend 55555
\begin{array}{l}\phantom{2225)}00024\phantom{10}\\2225\overline{)55555}\\\phantom{2225)}\underline{\phantom{}4450\phantom{9}}\\\phantom{2225)}11055\\\phantom{2225)}\underline{\phantom{9}8900\phantom{}}\\\phantom{2225)9}2155\\\end{array}
Find closest multiple of 2225 to 11055. We see that 4 \times 2225 = 8900 is the nearest. Now subtract 8900 from 11055 to get reminder 2155. Add 4 to quotient.
\text{Quotient: }24 \text{Reminder: }2155
Since 2155 is less than 2225, stop the division. The reminder is 2155. The topmost line 00024 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 24.
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}