Evaluate
7
Factor
7
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)189}\\\end{array}
Use the 1^{st} digit 1 from dividend 189
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)189}\\\end{array}
Since 1 is less than 27, use the next digit 8 from dividend 189 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)189}\\\end{array}
Use the 2^{nd} digit 8 from dividend 189
\begin{array}{l}\phantom{27)}00\phantom{4}\\27\overline{)189}\\\end{array}
Since 18 is less than 27, use the next digit 9 from dividend 189 and add 0 to the quotient
\begin{array}{l}\phantom{27)}00\phantom{5}\\27\overline{)189}\\\end{array}
Use the 3^{rd} digit 9 from dividend 189
\begin{array}{l}\phantom{27)}007\phantom{6}\\27\overline{)189}\\\phantom{27)}\underline{\phantom{}189\phantom{}}\\\phantom{27)999}0\\\end{array}
Find closest multiple of 27 to 189. We see that 7 \times 27 = 189 is the nearest. Now subtract 189 from 189 to get reminder 0. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }0
Since 0 is less than 27, stop the division. The reminder is 0. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}