Evaluate
\frac{80}{11}\approx 7.272727273
Factor
\frac{2 ^ {4} \cdot 5}{11} = 7\frac{3}{11} = 7.2727272727272725
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)240}\\\end{array}
Use the 1^{st} digit 2 from dividend 240
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)240}\\\end{array}
Since 2 is less than 33, use the next digit 4 from dividend 240 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)240}\\\end{array}
Use the 2^{nd} digit 4 from dividend 240
\begin{array}{l}\phantom{33)}00\phantom{4}\\33\overline{)240}\\\end{array}
Since 24 is less than 33, use the next digit 0 from dividend 240 and add 0 to the quotient
\begin{array}{l}\phantom{33)}00\phantom{5}\\33\overline{)240}\\\end{array}
Use the 3^{rd} digit 0 from dividend 240
\begin{array}{l}\phantom{33)}007\phantom{6}\\33\overline{)240}\\\phantom{33)}\underline{\phantom{}231\phantom{}}\\\phantom{33)99}9\\\end{array}
Find closest multiple of 33 to 240. We see that 7 \times 33 = 231 is the nearest. Now subtract 231 from 240 to get reminder 9. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }9
Since 9 is less than 33, stop the division. The reminder is 9. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}