Evaluate
\frac{1111}{90}\approx 12.344444444
Factor
\frac{11 \cdot 101}{2 \cdot 3 ^ {2} \cdot 5} = 12\frac{31}{90} = 12.344444444444445
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)1111}\\\end{array}
Use the 1^{st} digit 1 from dividend 1111
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)1111}\\\end{array}
Since 1 is less than 90, use the next digit 1 from dividend 1111 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)1111}\\\end{array}
Use the 2^{nd} digit 1 from dividend 1111
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)1111}\\\end{array}
Since 11 is less than 90, use the next digit 1 from dividend 1111 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)1111}\\\end{array}
Use the 3^{rd} digit 1 from dividend 1111
\begin{array}{l}\phantom{90)}001\phantom{6}\\90\overline{)1111}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}21\\\end{array}
Find closest multiple of 90 to 111. We see that 1 \times 90 = 90 is the nearest. Now subtract 90 from 111 to get reminder 21. Add 1 to quotient.
\begin{array}{l}\phantom{90)}001\phantom{7}\\90\overline{)1111}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}211\\\end{array}
Use the 4^{th} digit 1 from dividend 1111
\begin{array}{l}\phantom{90)}0012\phantom{8}\\90\overline{)1111}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}211\\\phantom{90)}\underline{\phantom{9}180\phantom{}}\\\phantom{90)99}31\\\end{array}
Find closest multiple of 90 to 211. We see that 2 \times 90 = 180 is the nearest. Now subtract 180 from 211 to get reminder 31. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }31
Since 31 is less than 90, stop the division. The reminder is 31. 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}