Evaluate
\frac{125}{26}\approx 4.807692308
Factor
\frac{5 ^ {3}}{2 \cdot 13} = 4\frac{21}{26} = 4.8076923076923075
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\begin{array}{l}\phantom{52)}\phantom{1}\\52\overline{)250}\\\end{array}
Use the 1^{st} digit 2 from dividend 250
\begin{array}{l}\phantom{52)}0\phantom{2}\\52\overline{)250}\\\end{array}
Since 2 is less than 52, use the next digit 5 from dividend 250 and add 0 to the quotient
\begin{array}{l}\phantom{52)}0\phantom{3}\\52\overline{)250}\\\end{array}
Use the 2^{nd} digit 5 from dividend 250
\begin{array}{l}\phantom{52)}00\phantom{4}\\52\overline{)250}\\\end{array}
Since 25 is less than 52, use the next digit 0 from dividend 250 and add 0 to the quotient
\begin{array}{l}\phantom{52)}00\phantom{5}\\52\overline{)250}\\\end{array}
Use the 3^{rd} digit 0 from dividend 250
\begin{array}{l}\phantom{52)}004\phantom{6}\\52\overline{)250}\\\phantom{52)}\underline{\phantom{}208\phantom{}}\\\phantom{52)9}42\\\end{array}
Find closest multiple of 52 to 250. We see that 4 \times 52 = 208 is the nearest. Now subtract 208 from 250 to get reminder 42. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }42
Since 42 is less than 52, stop the division. The reminder is 42. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}