Evaluate
\frac{31}{15}\approx 2.066666667
Factor
\frac{31}{3 \cdot 5} = 2\frac{1}{15} = 2.066666666666667
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)62}\\\end{array}
Use the 1^{st} digit 6 from dividend 62
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)62}\\\end{array}
Since 6 is less than 30, use the next digit 2 from dividend 62 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)62}\\\end{array}
Use the 2^{nd} digit 2 from dividend 62
\begin{array}{l}\phantom{30)}02\phantom{4}\\30\overline{)62}\\\phantom{30)}\underline{\phantom{}60\phantom{}}\\\phantom{30)9}2\\\end{array}
Find closest multiple of 30 to 62. We see that 2 \times 30 = 60 is the nearest. Now subtract 60 from 62 to get reminder 2. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }2
Since 2 is less than 30, stop the division. The reminder is 2. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}