Evaluate
\frac{41}{6}\approx 6.833333333
Factor
\frac{41}{2 \cdot 3} = 6\frac{5}{6} = 6.833333333333333
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)410}\\\end{array}
Use the 1^{st} digit 4 from dividend 410
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)410}\\\end{array}
Since 4 is less than 60, use the next digit 1 from dividend 410 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)410}\\\end{array}
Use the 2^{nd} digit 1 from dividend 410
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)410}\\\end{array}
Since 41 is less than 60, use the next digit 0 from dividend 410 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)410}\\\end{array}
Use the 3^{rd} digit 0 from dividend 410
\begin{array}{l}\phantom{60)}006\phantom{6}\\60\overline{)410}\\\phantom{60)}\underline{\phantom{}360\phantom{}}\\\phantom{60)9}50\\\end{array}
Find closest multiple of 60 to 410. We see that 6 \times 60 = 360 is the nearest. Now subtract 360 from 410 to get reminder 50. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }50
Since 50 is less than 60, stop the division. The reminder is 50. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}