Evaluate
\frac{221}{18}\approx 12.277777778
Factor
\frac{13 \cdot 17}{2 \cdot 3 ^ {2}} = 12\frac{5}{18} = 12.277777777777779
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)1105}\\\end{array}
Use the 1^{st} digit 1 from dividend 1105
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)1105}\\\end{array}
Since 1 is less than 90, use the next digit 1 from dividend 1105 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)1105}\\\end{array}
Use the 2^{nd} digit 1 from dividend 1105
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)1105}\\\end{array}
Since 11 is less than 90, use the next digit 0 from dividend 1105 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)1105}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1105
\begin{array}{l}\phantom{90)}001\phantom{6}\\90\overline{)1105}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}20\\\end{array}
Find closest multiple of 90 to 110. We see that 1 \times 90 = 90 is the nearest. Now subtract 90 from 110 to get reminder 20. Add 1 to quotient.
\begin{array}{l}\phantom{90)}001\phantom{7}\\90\overline{)1105}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}205\\\end{array}
Use the 4^{th} digit 5 from dividend 1105
\begin{array}{l}\phantom{90)}0012\phantom{8}\\90\overline{)1105}\\\phantom{90)}\underline{\phantom{9}90\phantom{9}}\\\phantom{90)9}205\\\phantom{90)}\underline{\phantom{9}180\phantom{}}\\\phantom{90)99}25\\\end{array}
Find closest multiple of 90 to 205. We see that 2 \times 90 = 180 is the nearest. Now subtract 180 from 205 to get reminder 25. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }25
Since 25 is less than 90, stop the division. The reminder is 25. 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}