Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{125)}\phantom{1}\\125\overline{)1500}\\\end{array}
Use the 1^{st} digit 1 from dividend 1500
\begin{array}{l}\phantom{125)}0\phantom{2}\\125\overline{)1500}\\\end{array}
Since 1 is less than 125, use the next digit 5 from dividend 1500 and add 0 to the quotient
\begin{array}{l}\phantom{125)}0\phantom{3}\\125\overline{)1500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1500
\begin{array}{l}\phantom{125)}00\phantom{4}\\125\overline{)1500}\\\end{array}
Since 15 is less than 125, use the next digit 0 from dividend 1500 and add 0 to the quotient
\begin{array}{l}\phantom{125)}00\phantom{5}\\125\overline{)1500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1500
\begin{array}{l}\phantom{125)}001\phantom{6}\\125\overline{)1500}\\\phantom{125)}\underline{\phantom{}125\phantom{9}}\\\phantom{125)9}25\\\end{array}
Find closest multiple of 125 to 150. We see that 1 \times 125 = 125 is the nearest. Now subtract 125 from 150 to get reminder 25. Add 1 to quotient.
\begin{array}{l}\phantom{125)}001\phantom{7}\\125\overline{)1500}\\\phantom{125)}\underline{\phantom{}125\phantom{9}}\\\phantom{125)9}250\\\end{array}
Use the 4^{th} digit 0 from dividend 1500
\begin{array}{l}\phantom{125)}0012\phantom{8}\\125\overline{)1500}\\\phantom{125)}\underline{\phantom{}125\phantom{9}}\\\phantom{125)9}250\\\phantom{125)}\underline{\phantom{9}250\phantom{}}\\\phantom{125)9999}0\\\end{array}
Find closest multiple of 125 to 250. We see that 2 \times 125 = 250 is the nearest. Now subtract 250 from 250 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 125, stop the division. The reminder is 0. The topmost line 0012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}