Evaluate
\frac{40}{11}\approx 3.636363636
Factor
\frac{2 ^ {3} \cdot 5}{11} = 3\frac{7}{11} = 3.6363636363636362
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\begin{array}{l}\phantom{220)}\phantom{1}\\220\overline{)800}\\\end{array}
Use the 1^{st} digit 8 from dividend 800
\begin{array}{l}\phantom{220)}0\phantom{2}\\220\overline{)800}\\\end{array}
Since 8 is less than 220, use the next digit 0 from dividend 800 and add 0 to the quotient
\begin{array}{l}\phantom{220)}0\phantom{3}\\220\overline{)800}\\\end{array}
Use the 2^{nd} digit 0 from dividend 800
\begin{array}{l}\phantom{220)}00\phantom{4}\\220\overline{)800}\\\end{array}
Since 80 is less than 220, use the next digit 0 from dividend 800 and add 0 to the quotient
\begin{array}{l}\phantom{220)}00\phantom{5}\\220\overline{)800}\\\end{array}
Use the 3^{rd} digit 0 from dividend 800
\begin{array}{l}\phantom{220)}003\phantom{6}\\220\overline{)800}\\\phantom{220)}\underline{\phantom{}660\phantom{}}\\\phantom{220)}140\\\end{array}
Find closest multiple of 220 to 800. We see that 3 \times 220 = 660 is the nearest. Now subtract 660 from 800 to get reminder 140. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }140
Since 140 is less than 220, stop the division. The reminder is 140. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}