Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)540}\\\end{array}
Use the 1^{st} digit 5 from dividend 540
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)540}\\\end{array}
Since 5 is less than 45, use the next digit 4 from dividend 540 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)540}\\\end{array}
Use the 2^{nd} digit 4 from dividend 540
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)540}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)9}9\\\end{array}
Find closest multiple of 45 to 54. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 54 to get reminder 9. Add 1 to quotient.
\begin{array}{l}\phantom{45)}01\phantom{5}\\45\overline{)540}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)9}90\\\end{array}
Use the 3^{rd} digit 0 from dividend 540
\begin{array}{l}\phantom{45)}012\phantom{6}\\45\overline{)540}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)9}90\\\phantom{45)}\underline{\phantom{9}90\phantom{}}\\\phantom{45)999}0\\\end{array}
Find closest multiple of 45 to 90. We see that 2 \times 45 = 90 is the nearest. Now subtract 90 from 90 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 45, stop the division. The reminder is 0. The topmost line 012 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}