Evaluate
\frac{130}{33}\approx 3.939393939
Factor
\frac{2 \cdot 5 \cdot 13}{3 \cdot 11} = 3\frac{31}{33} = 3.9393939393939394
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)130}\\\end{array}
Use the 1^{st} digit 1 from dividend 130
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)130}\\\end{array}
Since 1 is less than 33, use the next digit 3 from dividend 130 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)130}\\\end{array}
Use the 2^{nd} digit 3 from dividend 130
\begin{array}{l}\phantom{33)}00\phantom{4}\\33\overline{)130}\\\end{array}
Since 13 is less than 33, use the next digit 0 from dividend 130 and add 0 to the quotient
\begin{array}{l}\phantom{33)}00\phantom{5}\\33\overline{)130}\\\end{array}
Use the 3^{rd} digit 0 from dividend 130
\begin{array}{l}\phantom{33)}003\phantom{6}\\33\overline{)130}\\\phantom{33)}\underline{\phantom{9}99\phantom{}}\\\phantom{33)9}31\\\end{array}
Find closest multiple of 33 to 130. We see that 3 \times 33 = 99 is the nearest. Now subtract 99 from 130 to get reminder 31. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }31
Since 31 is less than 33, stop the division. The reminder is 31. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}