Evaluate
\frac{31}{4}=7.75
Factor
\frac{31}{2 ^ {2}} = 7\frac{3}{4} = 7.75
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)279}\\\end{array}
Use the 1^{st} digit 2 from dividend 279
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)279}\\\end{array}
Since 2 is less than 36, use the next digit 7 from dividend 279 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)279}\\\end{array}
Use the 2^{nd} digit 7 from dividend 279
\begin{array}{l}\phantom{36)}00\phantom{4}\\36\overline{)279}\\\end{array}
Since 27 is less than 36, use the next digit 9 from dividend 279 and add 0 to the quotient
\begin{array}{l}\phantom{36)}00\phantom{5}\\36\overline{)279}\\\end{array}
Use the 3^{rd} digit 9 from dividend 279
\begin{array}{l}\phantom{36)}007\phantom{6}\\36\overline{)279}\\\phantom{36)}\underline{\phantom{}252\phantom{}}\\\phantom{36)9}27\\\end{array}
Find closest multiple of 36 to 279. We see that 7 \times 36 = 252 is the nearest. Now subtract 252 from 279 to get reminder 27. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }27
Since 27 is less than 36, stop the division. The reminder is 27. 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}