Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)1080}\\\end{array}
Use the 1^{st} digit 1 from dividend 1080
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)1080}\\\end{array}
Since 1 is less than 90, use the next digit 0 from dividend 1080 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)1080}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1080
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)1080}\\\end{array}
Since 10 is less than 90, use the next digit 8 from dividend 1080 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)1080}\\\end{array}
Use the 3^{rd} digit 8 from dividend 1080
\begin{array}{l}\phantom{90)}001\phantom{6}\\90\overline{)1080}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}18\\\end{array}
Find closest multiple of 90 to 108. We see that 1 \times 90 = 90 is the nearest. Now subtract 90 from 108 to get reminder 18. Add 1 to quotient.
\begin{array}{l}\phantom{90)}001\phantom{7}\\90\overline{)1080}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}180\\\end{array}
Use the 4^{th} digit 0 from dividend 1080
\begin{array}{l}\phantom{90)}0012\phantom{8}\\90\overline{)1080}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}180\\\phantom{90)}\underline{\phantom{9}180\phantom{}}\\\phantom{90)9999}0\\\end{array}
Find closest multiple of 90 to 180. We see that 2 \times 90 = 180 is the nearest. Now subtract 180 from 180 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 90, 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}