Evaluate
\frac{243}{106}\approx 2.29245283
Factor
\frac{3 ^ {5}}{2 \cdot 53} = 2\frac{31}{106} = 2.292452830188679
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\begin{array}{l}\phantom{106)}\phantom{1}\\106\overline{)243}\\\end{array}
Use the 1^{st} digit 2 from dividend 243
\begin{array}{l}\phantom{106)}0\phantom{2}\\106\overline{)243}\\\end{array}
Since 2 is less than 106, use the next digit 4 from dividend 243 and add 0 to the quotient
\begin{array}{l}\phantom{106)}0\phantom{3}\\106\overline{)243}\\\end{array}
Use the 2^{nd} digit 4 from dividend 243
\begin{array}{l}\phantom{106)}00\phantom{4}\\106\overline{)243}\\\end{array}
Since 24 is less than 106, use the next digit 3 from dividend 243 and add 0 to the quotient
\begin{array}{l}\phantom{106)}00\phantom{5}\\106\overline{)243}\\\end{array}
Use the 3^{rd} digit 3 from dividend 243
\begin{array}{l}\phantom{106)}002\phantom{6}\\106\overline{)243}\\\phantom{106)}\underline{\phantom{}212\phantom{}}\\\phantom{106)9}31\\\end{array}
Find closest multiple of 106 to 243. We see that 2 \times 106 = 212 is the nearest. Now subtract 212 from 243 to get reminder 31. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }31
Since 31 is less than 106, stop the division. The reminder is 31. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}