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\begin{array}{l}\phantom{125)}\phantom{1}\\125\overline{)125}\\\end{array}
Use the 1^{st} digit 1 from dividend 125
\begin{array}{l}\phantom{125)}0\phantom{2}\\125\overline{)125}\\\end{array}
Since 1 is less than 125, use the next digit 2 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{125)}0\phantom{3}\\125\overline{)125}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125
\begin{array}{l}\phantom{125)}00\phantom{4}\\125\overline{)125}\\\end{array}
Since 12 is less than 125, use the next digit 5 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{125)}00\phantom{5}\\125\overline{)125}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125
\begin{array}{l}\phantom{125)}001\phantom{6}\\125\overline{)125}\\\phantom{125)}\underline{\phantom{}125\phantom{}}\\\phantom{125)999}0\\\end{array}
Find closest multiple of 125 to 125. We see that 1 \times 125 = 125 is the nearest. Now subtract 125 from 125 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }0
Since 0 is less than 125, stop the division. The reminder is 0. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}