Evaluate
\frac{125}{18}\approx 6.944444444
Factor
\frac{5 ^ {3}}{2 \cdot 3 ^ {2}} = 6\frac{17}{18} = 6.944444444444445
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\begin{array}{l}\phantom{900)}\phantom{1}\\900\overline{)6250}\\\end{array}
Use the 1^{st} digit 6 from dividend 6250
\begin{array}{l}\phantom{900)}0\phantom{2}\\900\overline{)6250}\\\end{array}
Since 6 is less than 900, use the next digit 2 from dividend 6250 and add 0 to the quotient
\begin{array}{l}\phantom{900)}0\phantom{3}\\900\overline{)6250}\\\end{array}
Use the 2^{nd} digit 2 from dividend 6250
\begin{array}{l}\phantom{900)}00\phantom{4}\\900\overline{)6250}\\\end{array}
Since 62 is less than 900, use the next digit 5 from dividend 6250 and add 0 to the quotient
\begin{array}{l}\phantom{900)}00\phantom{5}\\900\overline{)6250}\\\end{array}
Use the 3^{rd} digit 5 from dividend 6250
\begin{array}{l}\phantom{900)}000\phantom{6}\\900\overline{)6250}\\\end{array}
Since 625 is less than 900, use the next digit 0 from dividend 6250 and add 0 to the quotient
\begin{array}{l}\phantom{900)}000\phantom{7}\\900\overline{)6250}\\\end{array}
Use the 4^{th} digit 0 from dividend 6250
\begin{array}{l}\phantom{900)}0006\phantom{8}\\900\overline{)6250}\\\phantom{900)}\underline{\phantom{}5400\phantom{}}\\\phantom{900)9}850\\\end{array}
Find closest multiple of 900 to 6250. We see that 6 \times 900 = 5400 is the nearest. Now subtract 5400 from 6250 to get reminder 850. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }850
Since 850 is less than 900, stop the division. The reminder is 850. The topmost line 0006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}