Evaluate
\frac{5}{3}\approx 1.666666667
Factor
\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)55}\\\end{array}
Use the 1^{st} digit 5 from dividend 55
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)55}\\\end{array}
Since 5 is less than 33, use the next digit 5 from dividend 55 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)55}\\\end{array}
Use the 2^{nd} digit 5 from dividend 55
\begin{array}{l}\phantom{33)}01\phantom{4}\\33\overline{)55}\\\phantom{33)}\underline{\phantom{}33\phantom{}}\\\phantom{33)}22\\\end{array}
Find closest multiple of 33 to 55. We see that 1 \times 33 = 33 is the nearest. Now subtract 33 from 55 to get reminder 22. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }22
Since 22 is less than 33, stop the division. The reminder is 22. The topmost line 01 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}