Evaluate
9
Factor
3^{2}
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\begin{array}{l}\phantom{19)}\phantom{1}\\19\overline{)171}\\\end{array}
Use the 1^{st} digit 1 from dividend 171
\begin{array}{l}\phantom{19)}0\phantom{2}\\19\overline{)171}\\\end{array}
Since 1 is less than 19, use the next digit 7 from dividend 171 and add 0 to the quotient
\begin{array}{l}\phantom{19)}0\phantom{3}\\19\overline{)171}\\\end{array}
Use the 2^{nd} digit 7 from dividend 171
\begin{array}{l}\phantom{19)}00\phantom{4}\\19\overline{)171}\\\end{array}
Since 17 is less than 19, use the next digit 1 from dividend 171 and add 0 to the quotient
\begin{array}{l}\phantom{19)}00\phantom{5}\\19\overline{)171}\\\end{array}
Use the 3^{rd} digit 1 from dividend 171
\begin{array}{l}\phantom{19)}009\phantom{6}\\19\overline{)171}\\\phantom{19)}\underline{\phantom{}171\phantom{}}\\\phantom{19)999}0\\\end{array}
Find closest multiple of 19 to 171. We see that 9 \times 19 = 171 is the nearest. Now subtract 171 from 171 to get reminder 0. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }0
Since 0 is less than 19, stop the division. The reminder is 0. 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}