Evaluate
\frac{69}{22}\approx 3.136363636
Factor
\frac{3 \cdot 23}{2 \cdot 11} = 3\frac{3}{22} = 3.1363636363636362
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)69}\\\end{array}
Use the 1^{st} digit 6 from dividend 69
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)69}\\\end{array}
Since 6 is less than 22, use the next digit 9 from dividend 69 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)69}\\\end{array}
Use the 2^{nd} digit 9 from dividend 69
\begin{array}{l}\phantom{22)}03\phantom{4}\\22\overline{)69}\\\phantom{22)}\underline{\phantom{}66\phantom{}}\\\phantom{22)9}3\\\end{array}
Find closest multiple of 22 to 69. We see that 3 \times 22 = 66 is the nearest. Now subtract 66 from 69 to get reminder 3. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }3
Since 3 is less than 22, stop the division. The reminder is 3. The topmost line 03 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}