Evaluate
\frac{18109}{852}\approx 21.254694836
Factor
\frac{7 \cdot 13 \cdot 199}{2 ^ {2} \cdot 3 \cdot 71} = 21\frac{217}{852} = 21.254694835680752
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\begin{array}{l}\phantom{42600)}\phantom{1}\\42600\overline{)905450}\\\end{array}
Use the 1^{st} digit 9 from dividend 905450
\begin{array}{l}\phantom{42600)}0\phantom{2}\\42600\overline{)905450}\\\end{array}
Since 9 is less than 42600, use the next digit 0 from dividend 905450 and add 0 to the quotient
\begin{array}{l}\phantom{42600)}0\phantom{3}\\42600\overline{)905450}\\\end{array}
Use the 2^{nd} digit 0 from dividend 905450
\begin{array}{l}\phantom{42600)}00\phantom{4}\\42600\overline{)905450}\\\end{array}
Since 90 is less than 42600, use the next digit 5 from dividend 905450 and add 0 to the quotient
\begin{array}{l}\phantom{42600)}00\phantom{5}\\42600\overline{)905450}\\\end{array}
Use the 3^{rd} digit 5 from dividend 905450
\begin{array}{l}\phantom{42600)}000\phantom{6}\\42600\overline{)905450}\\\end{array}
Since 905 is less than 42600, use the next digit 4 from dividend 905450 and add 0 to the quotient
\begin{array}{l}\phantom{42600)}000\phantom{7}\\42600\overline{)905450}\\\end{array}
Use the 4^{th} digit 4 from dividend 905450
\begin{array}{l}\phantom{42600)}0000\phantom{8}\\42600\overline{)905450}\\\end{array}
Since 9054 is less than 42600, use the next digit 5 from dividend 905450 and add 0 to the quotient
\begin{array}{l}\phantom{42600)}0000\phantom{9}\\42600\overline{)905450}\\\end{array}
Use the 5^{th} digit 5 from dividend 905450
\begin{array}{l}\phantom{42600)}00002\phantom{10}\\42600\overline{)905450}\\\phantom{42600)}\underline{\phantom{}85200\phantom{9}}\\\phantom{42600)9}5345\\\end{array}
Find closest multiple of 42600 to 90545. We see that 2 \times 42600 = 85200 is the nearest. Now subtract 85200 from 90545 to get reminder 5345. Add 2 to quotient.
\begin{array}{l}\phantom{42600)}00002\phantom{11}\\42600\overline{)905450}\\\phantom{42600)}\underline{\phantom{}85200\phantom{9}}\\\phantom{42600)9}53450\\\end{array}
Use the 6^{th} digit 0 from dividend 905450
\begin{array}{l}\phantom{42600)}000021\phantom{12}\\42600\overline{)905450}\\\phantom{42600)}\underline{\phantom{}85200\phantom{9}}\\\phantom{42600)9}53450\\\phantom{42600)}\underline{\phantom{9}42600\phantom{}}\\\phantom{42600)9}10850\\\end{array}
Find closest multiple of 42600 to 53450. We see that 1 \times 42600 = 42600 is the nearest. Now subtract 42600 from 53450 to get reminder 10850. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }10850
Since 10850 is less than 42600, stop the division. The reminder is 10850. The topmost line 000021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}