Evaluate
18
Factor
2\times 3^{2}
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)270}\\\end{array}
Use the 1^{st} digit 2 from dividend 270
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)270}\\\end{array}
Since 2 is less than 15, use the next digit 7 from dividend 270 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)270}\\\end{array}
Use the 2^{nd} digit 7 from dividend 270
\begin{array}{l}\phantom{15)}01\phantom{4}\\15\overline{)270}\\\phantom{15)}\underline{\phantom{}15\phantom{9}}\\\phantom{15)}12\\\end{array}
Find closest multiple of 15 to 27. We see that 1 \times 15 = 15 is the nearest. Now subtract 15 from 27 to get reminder 12. Add 1 to quotient.
\begin{array}{l}\phantom{15)}01\phantom{5}\\15\overline{)270}\\\phantom{15)}\underline{\phantom{}15\phantom{9}}\\\phantom{15)}120\\\end{array}
Use the 3^{rd} digit 0 from dividend 270
\begin{array}{l}\phantom{15)}018\phantom{6}\\15\overline{)270}\\\phantom{15)}\underline{\phantom{}15\phantom{9}}\\\phantom{15)}120\\\phantom{15)}\underline{\phantom{}120\phantom{}}\\\phantom{15)999}0\\\end{array}
Find closest multiple of 15 to 120. We see that 8 \times 15 = 120 is the nearest. Now subtract 120 from 120 to get reminder 0. Add 8 to quotient.
\text{Quotient: }18 \text{Reminder: }0
Since 0 is less than 15, stop the division. The reminder is 0. The topmost line 018 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 18.
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}