Evaluate
\frac{421}{20}=21.05
Factor
\frac{421}{2 ^ {2} \cdot 5} = 21\frac{1}{20} = 21.05
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)421}\\\end{array}
Use the 1^{st} digit 4 from dividend 421
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)421}\\\end{array}
Since 4 is less than 20, use the next digit 2 from dividend 421 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)421}\\\end{array}
Use the 2^{nd} digit 2 from dividend 421
\begin{array}{l}\phantom{20)}02\phantom{4}\\20\overline{)421}\\\phantom{20)}\underline{\phantom{}40\phantom{9}}\\\phantom{20)9}2\\\end{array}
Find closest multiple of 20 to 42. We see that 2 \times 20 = 40 is the nearest. Now subtract 40 from 42 to get reminder 2. Add 2 to quotient.
\begin{array}{l}\phantom{20)}02\phantom{5}\\20\overline{)421}\\\phantom{20)}\underline{\phantom{}40\phantom{9}}\\\phantom{20)9}21\\\end{array}
Use the 3^{rd} digit 1 from dividend 421
\begin{array}{l}\phantom{20)}021\phantom{6}\\20\overline{)421}\\\phantom{20)}\underline{\phantom{}40\phantom{9}}\\\phantom{20)9}21\\\phantom{20)}\underline{\phantom{9}20\phantom{}}\\\phantom{20)99}1\\\end{array}
Find closest multiple of 20 to 21. We see that 1 \times 20 = 20 is the nearest. Now subtract 20 from 21 to get reminder 1. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }1
Since 1 is less than 20, stop the division. The reminder is 1. The topmost line 021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}