Evaluate
\frac{31}{2}=15.5
Factor
\frac{31}{2} = 15\frac{1}{2} = 15.5
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)186}\\\end{array}
Use the 1^{st} digit 1 from dividend 186
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)186}\\\end{array}
Since 1 is less than 12, use the next digit 8 from dividend 186 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)186}\\\end{array}
Use the 2^{nd} digit 8 from dividend 186
\begin{array}{l}\phantom{12)}01\phantom{4}\\12\overline{)186}\\\phantom{12)}\underline{\phantom{}12\phantom{9}}\\\phantom{12)9}6\\\end{array}
Find closest multiple of 12 to 18. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 18 to get reminder 6. Add 1 to quotient.
\begin{array}{l}\phantom{12)}01\phantom{5}\\12\overline{)186}\\\phantom{12)}\underline{\phantom{}12\phantom{9}}\\\phantom{12)9}66\\\end{array}
Use the 3^{rd} digit 6 from dividend 186
\begin{array}{l}\phantom{12)}015\phantom{6}\\12\overline{)186}\\\phantom{12)}\underline{\phantom{}12\phantom{9}}\\\phantom{12)9}66\\\phantom{12)}\underline{\phantom{9}60\phantom{}}\\\phantom{12)99}6\\\end{array}
Find closest multiple of 12 to 66. We see that 5 \times 12 = 60 is the nearest. Now subtract 60 from 66 to get reminder 6. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }6
Since 6 is less than 12, stop the division. The reminder is 6. The topmost line 015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}