Evaluate
\frac{75}{17}\approx 4.411764706
Factor
\frac{3 \cdot 5 ^ {2}}{17} = 4\frac{7}{17} = 4.411764705882353
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\begin{array}{l}\phantom{68)}\phantom{1}\\68\overline{)300}\\\end{array}
Use the 1^{st} digit 3 from dividend 300
\begin{array}{l}\phantom{68)}0\phantom{2}\\68\overline{)300}\\\end{array}
Since 3 is less than 68, use the next digit 0 from dividend 300 and add 0 to the quotient
\begin{array}{l}\phantom{68)}0\phantom{3}\\68\overline{)300}\\\end{array}
Use the 2^{nd} digit 0 from dividend 300
\begin{array}{l}\phantom{68)}00\phantom{4}\\68\overline{)300}\\\end{array}
Since 30 is less than 68, use the next digit 0 from dividend 300 and add 0 to the quotient
\begin{array}{l}\phantom{68)}00\phantom{5}\\68\overline{)300}\\\end{array}
Use the 3^{rd} digit 0 from dividend 300
\begin{array}{l}\phantom{68)}004\phantom{6}\\68\overline{)300}\\\phantom{68)}\underline{\phantom{}272\phantom{}}\\\phantom{68)9}28\\\end{array}
Find closest multiple of 68 to 300. We see that 4 \times 68 = 272 is the nearest. Now subtract 272 from 300 to get reminder 28. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }28
Since 28 is less than 68, stop the division. The reminder is 28. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}