Evaluate
\frac{41}{30}\approx 1.366666667
Factor
\frac{41}{2 \cdot 3 \cdot 5} = 1\frac{11}{30} = 1.3666666666666667
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)41}\\\end{array}
Use the 1^{st} digit 4 from dividend 41
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)41}\\\end{array}
Since 4 is less than 30, use the next digit 1 from dividend 41 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)41}\\\end{array}
Use the 2^{nd} digit 1 from dividend 41
\begin{array}{l}\phantom{30)}01\phantom{4}\\30\overline{)41}\\\phantom{30)}\underline{\phantom{}30\phantom{}}\\\phantom{30)}11\\\end{array}
Find closest multiple of 30 to 41. We see that 1 \times 30 = 30 is the nearest. Now subtract 30 from 41 to get reminder 11. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }11
Since 11 is less than 30, stop the division. The reminder is 11. 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}