Evaluate
\frac{48}{11}\approx 4.363636364
Factor
\frac{2 ^ {4} \cdot 3}{11} = 4\frac{4}{11} = 4.363636363636363
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)144}\\\end{array}
Use the 1^{st} digit 1 from dividend 144
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)144}\\\end{array}
Since 1 is less than 33, use the next digit 4 from dividend 144 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)144}\\\end{array}
Use the 2^{nd} digit 4 from dividend 144
\begin{array}{l}\phantom{33)}00\phantom{4}\\33\overline{)144}\\\end{array}
Since 14 is less than 33, use the next digit 4 from dividend 144 and add 0 to the quotient
\begin{array}{l}\phantom{33)}00\phantom{5}\\33\overline{)144}\\\end{array}
Use the 3^{rd} digit 4 from dividend 144
\begin{array}{l}\phantom{33)}004\phantom{6}\\33\overline{)144}\\\phantom{33)}\underline{\phantom{}132\phantom{}}\\\phantom{33)9}12\\\end{array}
Find closest multiple of 33 to 144. We see that 4 \times 33 = 132 is the nearest. Now subtract 132 from 144 to get reminder 12. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }12
Since 12 is less than 33, stop the division. The reminder is 12. 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}