Evaluate
\frac{31}{2}=15.5
Factor
\frac{31}{2} = 15\frac{1}{2} = 15.5
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)279}\\\end{array}
Use the 1^{st} digit 2 from dividend 279
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)279}\\\end{array}
Since 2 is less than 18, use the next digit 7 from dividend 279 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)279}\\\end{array}
Use the 2^{nd} digit 7 from dividend 279
\begin{array}{l}\phantom{18)}01\phantom{4}\\18\overline{)279}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}9\\\end{array}
Find closest multiple of 18 to 27. We see that 1 \times 18 = 18 is the nearest. Now subtract 18 from 27 to get reminder 9. Add 1 to quotient.
\begin{array}{l}\phantom{18)}01\phantom{5}\\18\overline{)279}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}99\\\end{array}
Use the 3^{rd} digit 9 from dividend 279
\begin{array}{l}\phantom{18)}015\phantom{6}\\18\overline{)279}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}99\\\phantom{18)}\underline{\phantom{9}90\phantom{}}\\\phantom{18)99}9\\\end{array}
Find closest multiple of 18 to 99. We see that 5 \times 18 = 90 is the nearest. Now subtract 90 from 99 to get reminder 9. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }9
Since 9 is less than 18, stop the division. The reminder is 9. 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}