Evaluate
\frac{80}{17}\approx 4.705882353
Factor
\frac{2 ^ {4} \cdot 5}{17} = 4\frac{12}{17} = 4.705882352941177
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)400}\\\end{array}
Use the 1^{st} digit 4 from dividend 400
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)400}\\\end{array}
Since 4 is less than 85, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)400}\\\end{array}
Use the 2^{nd} digit 0 from dividend 400
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)400}\\\end{array}
Since 40 is less than 85, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)400}\\\end{array}
Use the 3^{rd} digit 0 from dividend 400
\begin{array}{l}\phantom{85)}004\phantom{6}\\85\overline{)400}\\\phantom{85)}\underline{\phantom{}340\phantom{}}\\\phantom{85)9}60\\\end{array}
Find closest multiple of 85 to 400. We see that 4 \times 85 = 340 is the nearest. Now subtract 340 from 400 to get reminder 60. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }60
Since 60 is less than 85, stop the division. The reminder is 60. 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}