Evaluate
\frac{125}{51}\approx 2.450980392
Factor
\frac{5 ^ {3}}{3 \cdot 17} = 2\frac{23}{51} = 2.450980392156863
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\begin{array}{l}\phantom{102)}\phantom{1}\\102\overline{)250}\\\end{array}
Use the 1^{st} digit 2 from dividend 250
\begin{array}{l}\phantom{102)}0\phantom{2}\\102\overline{)250}\\\end{array}
Since 2 is less than 102, use the next digit 5 from dividend 250 and add 0 to the quotient
\begin{array}{l}\phantom{102)}0\phantom{3}\\102\overline{)250}\\\end{array}
Use the 2^{nd} digit 5 from dividend 250
\begin{array}{l}\phantom{102)}00\phantom{4}\\102\overline{)250}\\\end{array}
Since 25 is less than 102, use the next digit 0 from dividend 250 and add 0 to the quotient
\begin{array}{l}\phantom{102)}00\phantom{5}\\102\overline{)250}\\\end{array}
Use the 3^{rd} digit 0 from dividend 250
\begin{array}{l}\phantom{102)}002\phantom{6}\\102\overline{)250}\\\phantom{102)}\underline{\phantom{}204\phantom{}}\\\phantom{102)9}46\\\end{array}
Find closest multiple of 102 to 250. We see that 2 \times 102 = 204 is the nearest. Now subtract 204 from 250 to get reminder 46. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }46
Since 46 is less than 102, stop the division. The reminder is 46. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}