Evaluate
\frac{46}{31}\approx 1.483870968
Factor
\frac{2 \cdot 23}{31} = 1\frac{15}{31} = 1.4838709677419355
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\begin{array}{l}\phantom{31)}\phantom{1}\\31\overline{)46}\\\end{array}
Use the 1^{st} digit 4 from dividend 46
\begin{array}{l}\phantom{31)}0\phantom{2}\\31\overline{)46}\\\end{array}
Since 4 is less than 31, use the next digit 6 from dividend 46 and add 0 to the quotient
\begin{array}{l}\phantom{31)}0\phantom{3}\\31\overline{)46}\\\end{array}
Use the 2^{nd} digit 6 from dividend 46
\begin{array}{l}\phantom{31)}01\phantom{4}\\31\overline{)46}\\\phantom{31)}\underline{\phantom{}31\phantom{}}\\\phantom{31)}15\\\end{array}
Find closest multiple of 31 to 46. We see that 1 \times 31 = 31 is the nearest. Now subtract 31 from 46 to get reminder 15. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }15
Since 15 is less than 31, stop the division. The reminder is 15. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}