Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{1125)}\phantom{1}\\1125\overline{)13500}\\\end{array}
Use the 1^{st} digit 1 from dividend 13500
\begin{array}{l}\phantom{1125)}0\phantom{2}\\1125\overline{)13500}\\\end{array}
Since 1 is less than 1125, use the next digit 3 from dividend 13500 and add 0 to the quotient
\begin{array}{l}\phantom{1125)}0\phantom{3}\\1125\overline{)13500}\\\end{array}
Use the 2^{nd} digit 3 from dividend 13500
\begin{array}{l}\phantom{1125)}00\phantom{4}\\1125\overline{)13500}\\\end{array}
Since 13 is less than 1125, use the next digit 5 from dividend 13500 and add 0 to the quotient
\begin{array}{l}\phantom{1125)}00\phantom{5}\\1125\overline{)13500}\\\end{array}
Use the 3^{rd} digit 5 from dividend 13500
\begin{array}{l}\phantom{1125)}000\phantom{6}\\1125\overline{)13500}\\\end{array}
Since 135 is less than 1125, use the next digit 0 from dividend 13500 and add 0 to the quotient
\begin{array}{l}\phantom{1125)}000\phantom{7}\\1125\overline{)13500}\\\end{array}
Use the 4^{th} digit 0 from dividend 13500
\begin{array}{l}\phantom{1125)}0001\phantom{8}\\1125\overline{)13500}\\\phantom{1125)}\underline{\phantom{}1125\phantom{9}}\\\phantom{1125)9}225\\\end{array}
Find closest multiple of 1125 to 1350. We see that 1 \times 1125 = 1125 is the nearest. Now subtract 1125 from 1350 to get reminder 225. Add 1 to quotient.
\begin{array}{l}\phantom{1125)}0001\phantom{9}\\1125\overline{)13500}\\\phantom{1125)}\underline{\phantom{}1125\phantom{9}}\\\phantom{1125)9}2250\\\end{array}
Use the 5^{th} digit 0 from dividend 13500
\begin{array}{l}\phantom{1125)}00012\phantom{10}\\1125\overline{)13500}\\\phantom{1125)}\underline{\phantom{}1125\phantom{9}}\\\phantom{1125)9}2250\\\phantom{1125)}\underline{\phantom{9}2250\phantom{}}\\\phantom{1125)99999}0\\\end{array}
Find closest multiple of 1125 to 2250. We see that 2 \times 1125 = 2250 is the nearest. Now subtract 2250 from 2250 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 1125, stop the division. The reminder is 0. The topmost line 00012 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}