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{40)}\phantom{1}\\40\overline{)310}\\\end{array}
Use the 1^{st} digit 3 from dividend 310
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)310}\\\end{array}
Since 3 is less than 40, use the next digit 1 from dividend 310 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)310}\\\end{array}
Use the 2^{nd} digit 1 from dividend 310
\begin{array}{l}\phantom{40)}00\phantom{4}\\40\overline{)310}\\\end{array}
Since 31 is less than 40, use the next digit 0 from dividend 310 and add 0 to the quotient
\begin{array}{l}\phantom{40)}00\phantom{5}\\40\overline{)310}\\\end{array}
Use the 3^{rd} digit 0 from dividend 310
\begin{array}{l}\phantom{40)}007\phantom{6}\\40\overline{)310}\\\phantom{40)}\underline{\phantom{}280\phantom{}}\\\phantom{40)9}30\\\end{array}
Find closest multiple of 40 to 310. We see that 7 \times 40 = 280 is the nearest. Now subtract 280 from 310 to get reminder 30. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }30
Since 30 is less than 40, stop the division. The reminder is 30. 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}