Evaluate
\frac{34}{5}=6.8
Factor
\frac{2 \cdot 17}{5} = 6\frac{4}{5} = 6.8
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)408}\\\end{array}
Use the 1^{st} digit 4 from dividend 408
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)408}\\\end{array}
Since 4 is less than 60, use the next digit 0 from dividend 408 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)408}\\\end{array}
Use the 2^{nd} digit 0 from dividend 408
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)408}\\\end{array}
Since 40 is less than 60, use the next digit 8 from dividend 408 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)408}\\\end{array}
Use the 3^{rd} digit 8 from dividend 408
\begin{array}{l}\phantom{60)}006\phantom{6}\\60\overline{)408}\\\phantom{60)}\underline{\phantom{}360\phantom{}}\\\phantom{60)9}48\\\end{array}
Find closest multiple of 60 to 408. We see that 6 \times 60 = 360 is the nearest. Now subtract 360 from 408 to get reminder 48. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }48
Since 48 is less than 60, stop the division. The reminder is 48. 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}