Evaluate
5
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5
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\begin{array}{l}\phantom{125)}\phantom{1}\\125\overline{)625}\\\end{array}
Use the 1^{st} digit 6 from dividend 625
\begin{array}{l}\phantom{125)}0\phantom{2}\\125\overline{)625}\\\end{array}
Since 6 is less than 125, use the next digit 2 from dividend 625 and add 0 to the quotient
\begin{array}{l}\phantom{125)}0\phantom{3}\\125\overline{)625}\\\end{array}
Use the 2^{nd} digit 2 from dividend 625
\begin{array}{l}\phantom{125)}00\phantom{4}\\125\overline{)625}\\\end{array}
Since 62 is less than 125, use the next digit 5 from dividend 625 and add 0 to the quotient
\begin{array}{l}\phantom{125)}00\phantom{5}\\125\overline{)625}\\\end{array}
Use the 3^{rd} digit 5 from dividend 625
\begin{array}{l}\phantom{125)}005\phantom{6}\\125\overline{)625}\\\phantom{125)}\underline{\phantom{}625\phantom{}}\\\phantom{125)999}0\\\end{array}
Find closest multiple of 125 to 625. We see that 5 \times 125 = 625 is the nearest. Now subtract 625 from 625 to get reminder 0. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }0
Since 0 is less than 125, stop the division. The reminder is 0. 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}