Evaluate
\frac{269}{66}\approx 4.075757576
Factor
\frac{269}{2 \cdot 3 \cdot 11} = 4\frac{5}{66} = 4.075757575757576
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\begin{array}{l}\phantom{66)}\phantom{1}\\66\overline{)269}\\\end{array}
Use the 1^{st} digit 2 from dividend 269
\begin{array}{l}\phantom{66)}0\phantom{2}\\66\overline{)269}\\\end{array}
Since 2 is less than 66, use the next digit 6 from dividend 269 and add 0 to the quotient
\begin{array}{l}\phantom{66)}0\phantom{3}\\66\overline{)269}\\\end{array}
Use the 2^{nd} digit 6 from dividend 269
\begin{array}{l}\phantom{66)}00\phantom{4}\\66\overline{)269}\\\end{array}
Since 26 is less than 66, use the next digit 9 from dividend 269 and add 0 to the quotient
\begin{array}{l}\phantom{66)}00\phantom{5}\\66\overline{)269}\\\end{array}
Use the 3^{rd} digit 9 from dividend 269
\begin{array}{l}\phantom{66)}004\phantom{6}\\66\overline{)269}\\\phantom{66)}\underline{\phantom{}264\phantom{}}\\\phantom{66)99}5\\\end{array}
Find closest multiple of 66 to 269. We see that 4 \times 66 = 264 is the nearest. Now subtract 264 from 269 to get reminder 5. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }5
Since 5 is less than 66, stop the division. The reminder is 5. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}