Evaluate
\frac{104}{15}\approx 6.933333333
Factor
\frac{2 ^ {3} \cdot 13}{3 \cdot 5} = 6\frac{14}{15} = 6.933333333333334
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)208}\\\end{array}
Use the 1^{st} digit 2 from dividend 208
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)208}\\\end{array}
Since 2 is less than 30, use the next digit 0 from dividend 208 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)208}\\\end{array}
Use the 2^{nd} digit 0 from dividend 208
\begin{array}{l}\phantom{30)}00\phantom{4}\\30\overline{)208}\\\end{array}
Since 20 is less than 30, use the next digit 8 from dividend 208 and add 0 to the quotient
\begin{array}{l}\phantom{30)}00\phantom{5}\\30\overline{)208}\\\end{array}
Use the 3^{rd} digit 8 from dividend 208
\begin{array}{l}\phantom{30)}006\phantom{6}\\30\overline{)208}\\\phantom{30)}\underline{\phantom{}180\phantom{}}\\\phantom{30)9}28\\\end{array}
Find closest multiple of 30 to 208. We see that 6 \times 30 = 180 is the nearest. Now subtract 180 from 208 to get reminder 28. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }28
Since 28 is less than 30, stop the division. The reminder is 28. 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}