Evaluate
\frac{684}{625}=1.0944
Factor
\frac{2 ^ {2} \cdot 3 ^ {2} \cdot 19}{5 ^ {4}} = 1\frac{59}{625} = 1.0944
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\begin{array}{l}\phantom{62500)}\phantom{1}\\62500\overline{)68400}\\\end{array}
Use the 1^{st} digit 6 from dividend 68400
\begin{array}{l}\phantom{62500)}0\phantom{2}\\62500\overline{)68400}\\\end{array}
Since 6 is less than 62500, use the next digit 8 from dividend 68400 and add 0 to the quotient
\begin{array}{l}\phantom{62500)}0\phantom{3}\\62500\overline{)68400}\\\end{array}
Use the 2^{nd} digit 8 from dividend 68400
\begin{array}{l}\phantom{62500)}00\phantom{4}\\62500\overline{)68400}\\\end{array}
Since 68 is less than 62500, use the next digit 4 from dividend 68400 and add 0 to the quotient
\begin{array}{l}\phantom{62500)}00\phantom{5}\\62500\overline{)68400}\\\end{array}
Use the 3^{rd} digit 4 from dividend 68400
\begin{array}{l}\phantom{62500)}000\phantom{6}\\62500\overline{)68400}\\\end{array}
Since 684 is less than 62500, use the next digit 0 from dividend 68400 and add 0 to the quotient
\begin{array}{l}\phantom{62500)}000\phantom{7}\\62500\overline{)68400}\\\end{array}
Use the 4^{th} digit 0 from dividend 68400
\begin{array}{l}\phantom{62500)}0000\phantom{8}\\62500\overline{)68400}\\\end{array}
Since 6840 is less than 62500, use the next digit 0 from dividend 68400 and add 0 to the quotient
\begin{array}{l}\phantom{62500)}0000\phantom{9}\\62500\overline{)68400}\\\end{array}
Use the 5^{th} digit 0 from dividend 68400
\begin{array}{l}\phantom{62500)}00001\phantom{10}\\62500\overline{)68400}\\\phantom{62500)}\underline{\phantom{}62500\phantom{}}\\\phantom{62500)9}5900\\\end{array}
Find closest multiple of 62500 to 68400. We see that 1 \times 62500 = 62500 is the nearest. Now subtract 62500 from 68400 to get reminder 5900. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }5900
Since 5900 is less than 62500, stop the division. The reminder is 5900. The topmost line 00001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}