Evaluate
\frac{82}{15}\approx 5.466666667
Factor
\frac{2 \cdot 41}{3 \cdot 5} = 5\frac{7}{15} = 5.466666666666667
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)328}\\\end{array}
Use the 1^{st} digit 3 from dividend 328
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)328}\\\end{array}
Since 3 is less than 60, use the next digit 2 from dividend 328 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)328}\\\end{array}
Use the 2^{nd} digit 2 from dividend 328
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)328}\\\end{array}
Since 32 is less than 60, use the next digit 8 from dividend 328 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)328}\\\end{array}
Use the 3^{rd} digit 8 from dividend 328
\begin{array}{l}\phantom{60)}005\phantom{6}\\60\overline{)328}\\\phantom{60)}\underline{\phantom{}300\phantom{}}\\\phantom{60)9}28\\\end{array}
Find closest multiple of 60 to 328. We see that 5 \times 60 = 300 is the nearest. Now subtract 300 from 328 to get reminder 28. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }28
Since 28 is less than 60, stop the division. The reminder is 28. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}