Evaluate
\frac{131}{31}\approx 4.225806452
Factor
\frac{131}{31} = 4\frac{7}{31} = 4.225806451612903
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\begin{array}{l}\phantom{62)}\phantom{1}\\62\overline{)262}\\\end{array}
Use the 1^{st} digit 2 from dividend 262
\begin{array}{l}\phantom{62)}0\phantom{2}\\62\overline{)262}\\\end{array}
Since 2 is less than 62, use the next digit 6 from dividend 262 and add 0 to the quotient
\begin{array}{l}\phantom{62)}0\phantom{3}\\62\overline{)262}\\\end{array}
Use the 2^{nd} digit 6 from dividend 262
\begin{array}{l}\phantom{62)}00\phantom{4}\\62\overline{)262}\\\end{array}
Since 26 is less than 62, use the next digit 2 from dividend 262 and add 0 to the quotient
\begin{array}{l}\phantom{62)}00\phantom{5}\\62\overline{)262}\\\end{array}
Use the 3^{rd} digit 2 from dividend 262
\begin{array}{l}\phantom{62)}004\phantom{6}\\62\overline{)262}\\\phantom{62)}\underline{\phantom{}248\phantom{}}\\\phantom{62)9}14\\\end{array}
Find closest multiple of 62 to 262. We see that 4 \times 62 = 248 is the nearest. Now subtract 248 from 262 to get reminder 14. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }14
Since 14 is less than 62, stop the division. The reminder is 14. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}