Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)180}\\\end{array}
Since 1 is less than 15, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{15)}01\phantom{4}\\15\overline{)180}\\\phantom{15)}\underline{\phantom{}15\phantom{9}}\\\phantom{15)9}3\\\end{array}
Find closest multiple of 15 to 18. We see that 1 \times 15 = 15 is the nearest. Now subtract 15 from 18 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{15)}01\phantom{5}\\15\overline{)180}\\\phantom{15)}\underline{\phantom{}15\phantom{9}}\\\phantom{15)9}30\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{15)}012\phantom{6}\\15\overline{)180}\\\phantom{15)}\underline{\phantom{}15\phantom{9}}\\\phantom{15)9}30\\\phantom{15)}\underline{\phantom{9}30\phantom{}}\\\phantom{15)999}0\\\end{array}
Find closest multiple of 15 to 30. We see that 2 \times 15 = 30 is the nearest. Now subtract 30 from 30 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 15, stop the division. The reminder is 0. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}