Evaluate
\frac{652}{125}=5.216
Factor
\frac{2 ^ {2} \cdot 163}{5 ^ {3}} = 5\frac{27}{125} = 5.216
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\begin{array}{l}\phantom{125)}\phantom{1}\\125\overline{)652}\\\end{array}
Use the 1^{st} digit 6 from dividend 652
\begin{array}{l}\phantom{125)}0\phantom{2}\\125\overline{)652}\\\end{array}
Since 6 is less than 125, use the next digit 5 from dividend 652 and add 0 to the quotient
\begin{array}{l}\phantom{125)}0\phantom{3}\\125\overline{)652}\\\end{array}
Use the 2^{nd} digit 5 from dividend 652
\begin{array}{l}\phantom{125)}00\phantom{4}\\125\overline{)652}\\\end{array}
Since 65 is less than 125, use the next digit 2 from dividend 652 and add 0 to the quotient
\begin{array}{l}\phantom{125)}00\phantom{5}\\125\overline{)652}\\\end{array}
Use the 3^{rd} digit 2 from dividend 652
\begin{array}{l}\phantom{125)}005\phantom{6}\\125\overline{)652}\\\phantom{125)}\underline{\phantom{}625\phantom{}}\\\phantom{125)9}27\\\end{array}
Find closest multiple of 125 to 652. We see that 5 \times 125 = 625 is the nearest. Now subtract 625 from 652 to get reminder 27. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }27
Since 27 is less than 125, stop the division. The reminder is 27. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}