Evaluate
\frac{4021}{85}\approx 47.305882353
Factor
\frac{4021}{5 \cdot 17} = 47\frac{26}{85} = 47.305882352941175
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)4021}\\\end{array}
Use the 1^{st} digit 4 from dividend 4021
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)4021}\\\end{array}
Since 4 is less than 85, use the next digit 0 from dividend 4021 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)4021}\\\end{array}
Use the 2^{nd} digit 0 from dividend 4021
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)4021}\\\end{array}
Since 40 is less than 85, use the next digit 2 from dividend 4021 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)4021}\\\end{array}
Use the 3^{rd} digit 2 from dividend 4021
\begin{array}{l}\phantom{85)}004\phantom{6}\\85\overline{)4021}\\\phantom{85)}\underline{\phantom{}340\phantom{9}}\\\phantom{85)9}62\\\end{array}
Find closest multiple of 85 to 402. We see that 4 \times 85 = 340 is the nearest. Now subtract 340 from 402 to get reminder 62. Add 4 to quotient.
\begin{array}{l}\phantom{85)}004\phantom{7}\\85\overline{)4021}\\\phantom{85)}\underline{\phantom{}340\phantom{9}}\\\phantom{85)9}621\\\end{array}
Use the 4^{th} digit 1 from dividend 4021
\begin{array}{l}\phantom{85)}0047\phantom{8}\\85\overline{)4021}\\\phantom{85)}\underline{\phantom{}340\phantom{9}}\\\phantom{85)9}621\\\phantom{85)}\underline{\phantom{9}595\phantom{}}\\\phantom{85)99}26\\\end{array}
Find closest multiple of 85 to 621. We see that 7 \times 85 = 595 is the nearest. Now subtract 595 from 621 to get reminder 26. Add 7 to quotient.
\text{Quotient: }47 \text{Reminder: }26
Since 26 is less than 85, stop the division. The reminder is 26. The topmost line 0047 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 47.
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}