Evaluate
29
Factor
29
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)609}\\\end{array}
Use the 1^{st} digit 6 from dividend 609
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)609}\\\end{array}
Since 6 is less than 21, use the next digit 0 from dividend 609 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)609}\\\end{array}
Use the 2^{nd} digit 0 from dividend 609
\begin{array}{l}\phantom{21)}02\phantom{4}\\21\overline{)609}\\\phantom{21)}\underline{\phantom{}42\phantom{9}}\\\phantom{21)}18\\\end{array}
Find closest multiple of 21 to 60. We see that 2 \times 21 = 42 is the nearest. Now subtract 42 from 60 to get reminder 18. Add 2 to quotient.
\begin{array}{l}\phantom{21)}02\phantom{5}\\21\overline{)609}\\\phantom{21)}\underline{\phantom{}42\phantom{9}}\\\phantom{21)}189\\\end{array}
Use the 3^{rd} digit 9 from dividend 609
\begin{array}{l}\phantom{21)}029\phantom{6}\\21\overline{)609}\\\phantom{21)}\underline{\phantom{}42\phantom{9}}\\\phantom{21)}189\\\phantom{21)}\underline{\phantom{}189\phantom{}}\\\phantom{21)999}0\\\end{array}
Find closest multiple of 21 to 189. We see that 9 \times 21 = 189 is the nearest. Now subtract 189 from 189 to get reminder 0. Add 9 to quotient.
\text{Quotient: }29 \text{Reminder: }0
Since 0 is less than 21, stop the division. The reminder is 0. The topmost line 029 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 29.
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}