Evaluate
\frac{275}{243}\approx 1.131687243
Factor
\frac{5 ^ {2} \cdot 11}{3 ^ {5}} = 1\frac{32}{243} = 1.131687242798354
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\begin{array}{l}\phantom{243)}\phantom{1}\\243\overline{)275}\\\end{array}
Use the 1^{st} digit 2 from dividend 275
\begin{array}{l}\phantom{243)}0\phantom{2}\\243\overline{)275}\\\end{array}
Since 2 is less than 243, use the next digit 7 from dividend 275 and add 0 to the quotient
\begin{array}{l}\phantom{243)}0\phantom{3}\\243\overline{)275}\\\end{array}
Use the 2^{nd} digit 7 from dividend 275
\begin{array}{l}\phantom{243)}00\phantom{4}\\243\overline{)275}\\\end{array}
Since 27 is less than 243, use the next digit 5 from dividend 275 and add 0 to the quotient
\begin{array}{l}\phantom{243)}00\phantom{5}\\243\overline{)275}\\\end{array}
Use the 3^{rd} digit 5 from dividend 275
\begin{array}{l}\phantom{243)}001\phantom{6}\\243\overline{)275}\\\phantom{243)}\underline{\phantom{}243\phantom{}}\\\phantom{243)9}32\\\end{array}
Find closest multiple of 243 to 275. We see that 1 \times 243 = 243 is the nearest. Now subtract 243 from 275 to get reminder 32. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }32
Since 32 is less than 243, stop the division. The reminder is 32. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}