Evaluate
\frac{6428}{1885}\approx 3.410079576
Factor
\frac{2 ^ {2} \cdot 1607}{5 \cdot 13 \cdot 29} = 3\frac{773}{1885} = 3.410079575596817
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\begin{array}{l}\phantom{94250)}\phantom{1}\\94250\overline{)321400}\\\end{array}
Use the 1^{st} digit 3 from dividend 321400
\begin{array}{l}\phantom{94250)}0\phantom{2}\\94250\overline{)321400}\\\end{array}
Since 3 is less than 94250, use the next digit 2 from dividend 321400 and add 0 to the quotient
\begin{array}{l}\phantom{94250)}0\phantom{3}\\94250\overline{)321400}\\\end{array}
Use the 2^{nd} digit 2 from dividend 321400
\begin{array}{l}\phantom{94250)}00\phantom{4}\\94250\overline{)321400}\\\end{array}
Since 32 is less than 94250, use the next digit 1 from dividend 321400 and add 0 to the quotient
\begin{array}{l}\phantom{94250)}00\phantom{5}\\94250\overline{)321400}\\\end{array}
Use the 3^{rd} digit 1 from dividend 321400
\begin{array}{l}\phantom{94250)}000\phantom{6}\\94250\overline{)321400}\\\end{array}
Since 321 is less than 94250, use the next digit 4 from dividend 321400 and add 0 to the quotient
\begin{array}{l}\phantom{94250)}000\phantom{7}\\94250\overline{)321400}\\\end{array}
Use the 4^{th} digit 4 from dividend 321400
\begin{array}{l}\phantom{94250)}0000\phantom{8}\\94250\overline{)321400}\\\end{array}
Since 3214 is less than 94250, use the next digit 0 from dividend 321400 and add 0 to the quotient
\begin{array}{l}\phantom{94250)}0000\phantom{9}\\94250\overline{)321400}\\\end{array}
Use the 5^{th} digit 0 from dividend 321400
\begin{array}{l}\phantom{94250)}00000\phantom{10}\\94250\overline{)321400}\\\end{array}
Since 32140 is less than 94250, use the next digit 0 from dividend 321400 and add 0 to the quotient
\begin{array}{l}\phantom{94250)}00000\phantom{11}\\94250\overline{)321400}\\\end{array}
Use the 6^{th} digit 0 from dividend 321400
\begin{array}{l}\phantom{94250)}000003\phantom{12}\\94250\overline{)321400}\\\phantom{94250)}\underline{\phantom{}282750\phantom{}}\\\phantom{94250)9}38650\\\end{array}
Find closest multiple of 94250 to 321400. We see that 3 \times 94250 = 282750 is the nearest. Now subtract 282750 from 321400 to get reminder 38650. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }38650
Since 38650 is less than 94250, stop the division. The reminder is 38650. The topmost line 000003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}