Evaluate
\frac{3906}{3125}=1.24992
Factor
\frac{2 \cdot 3 ^ {2} \cdot 7 \cdot 31}{5 ^ {5}} = 1\frac{781}{3125} = 1.24992
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\begin{array}{l}\phantom{3125)}\phantom{1}\\3125\overline{)3906}\\\end{array}
Use the 1^{st} digit 3 from dividend 3906
\begin{array}{l}\phantom{3125)}0\phantom{2}\\3125\overline{)3906}\\\end{array}
Since 3 is less than 3125, use the next digit 9 from dividend 3906 and add 0 to the quotient
\begin{array}{l}\phantom{3125)}0\phantom{3}\\3125\overline{)3906}\\\end{array}
Use the 2^{nd} digit 9 from dividend 3906
\begin{array}{l}\phantom{3125)}00\phantom{4}\\3125\overline{)3906}\\\end{array}
Since 39 is less than 3125, use the next digit 0 from dividend 3906 and add 0 to the quotient
\begin{array}{l}\phantom{3125)}00\phantom{5}\\3125\overline{)3906}\\\end{array}
Use the 3^{rd} digit 0 from dividend 3906
\begin{array}{l}\phantom{3125)}000\phantom{6}\\3125\overline{)3906}\\\end{array}
Since 390 is less than 3125, use the next digit 6 from dividend 3906 and add 0 to the quotient
\begin{array}{l}\phantom{3125)}000\phantom{7}\\3125\overline{)3906}\\\end{array}
Use the 4^{th} digit 6 from dividend 3906
\begin{array}{l}\phantom{3125)}0001\phantom{8}\\3125\overline{)3906}\\\phantom{3125)}\underline{\phantom{}3125\phantom{}}\\\phantom{3125)9}781\\\end{array}
Find closest multiple of 3125 to 3906. We see that 1 \times 3125 = 3125 is the nearest. Now subtract 3125 from 3906 to get reminder 781. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }781
Since 781 is less than 3125, stop the division. The reminder is 781. The topmost line 0001 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}