Evaluate
\frac{381}{7}\approx 54.428571429
Factor
\frac{3 \cdot 127}{7} = 54\frac{3}{7} = 54.42857142857143
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)1143}\\\end{array}
Use the 1^{st} digit 1 from dividend 1143
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)1143}\\\end{array}
Since 1 is less than 21, use the next digit 1 from dividend 1143 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)1143}\\\end{array}
Use the 2^{nd} digit 1 from dividend 1143
\begin{array}{l}\phantom{21)}00\phantom{4}\\21\overline{)1143}\\\end{array}
Since 11 is less than 21, use the next digit 4 from dividend 1143 and add 0 to the quotient
\begin{array}{l}\phantom{21)}00\phantom{5}\\21\overline{)1143}\\\end{array}
Use the 3^{rd} digit 4 from dividend 1143
\begin{array}{l}\phantom{21)}005\phantom{6}\\21\overline{)1143}\\\phantom{21)}\underline{\phantom{}105\phantom{9}}\\\phantom{21)99}9\\\end{array}
Find closest multiple of 21 to 114. We see that 5 \times 21 = 105 is the nearest. Now subtract 105 from 114 to get reminder 9. Add 5 to quotient.
\begin{array}{l}\phantom{21)}005\phantom{7}\\21\overline{)1143}\\\phantom{21)}\underline{\phantom{}105\phantom{9}}\\\phantom{21)99}93\\\end{array}
Use the 4^{th} digit 3 from dividend 1143
\begin{array}{l}\phantom{21)}0054\phantom{8}\\21\overline{)1143}\\\phantom{21)}\underline{\phantom{}105\phantom{9}}\\\phantom{21)99}93\\\phantom{21)}\underline{\phantom{99}84\phantom{}}\\\phantom{21)999}9\\\end{array}
Find closest multiple of 21 to 93. We see that 4 \times 21 = 84 is the nearest. Now subtract 84 from 93 to get reminder 9. Add 4 to quotient.
\text{Quotient: }54 \text{Reminder: }9
Since 9 is less than 21, stop the division. The reminder is 9. The topmost line 0054 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 54.
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}