Evaluate
\frac{29}{3}\approx 9.666666667
Factor
\frac{29}{3} = 9\frac{2}{3} = 9.666666666666666
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)203}\\\end{array}
Use the 1^{st} digit 2 from dividend 203
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)203}\\\end{array}
Since 2 is less than 21, use the next digit 0 from dividend 203 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)203}\\\end{array}
Use the 2^{nd} digit 0 from dividend 203
\begin{array}{l}\phantom{21)}00\phantom{4}\\21\overline{)203}\\\end{array}
Since 20 is less than 21, use the next digit 3 from dividend 203 and add 0 to the quotient
\begin{array}{l}\phantom{21)}00\phantom{5}\\21\overline{)203}\\\end{array}
Use the 3^{rd} digit 3 from dividend 203
\begin{array}{l}\phantom{21)}009\phantom{6}\\21\overline{)203}\\\phantom{21)}\underline{\phantom{}189\phantom{}}\\\phantom{21)9}14\\\end{array}
Find closest multiple of 21 to 203. We see that 9 \times 21 = 189 is the nearest. Now subtract 189 from 203 to get reminder 14. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }14
Since 14 is less than 21, stop the division. The reminder is 14. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}