Evaluate
\frac{129}{31}\approx 4.161290323
Factor
\frac{3 \cdot 43}{31} = 4\frac{5}{31} = 4.161290322580645
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\begin{array}{l}\phantom{31)}\phantom{1}\\31\overline{)129}\\\end{array}
Use the 1^{st} digit 1 from dividend 129
\begin{array}{l}\phantom{31)}0\phantom{2}\\31\overline{)129}\\\end{array}
Since 1 is less than 31, use the next digit 2 from dividend 129 and add 0 to the quotient
\begin{array}{l}\phantom{31)}0\phantom{3}\\31\overline{)129}\\\end{array}
Use the 2^{nd} digit 2 from dividend 129
\begin{array}{l}\phantom{31)}00\phantom{4}\\31\overline{)129}\\\end{array}
Since 12 is less than 31, use the next digit 9 from dividend 129 and add 0 to the quotient
\begin{array}{l}\phantom{31)}00\phantom{5}\\31\overline{)129}\\\end{array}
Use the 3^{rd} digit 9 from dividend 129
\begin{array}{l}\phantom{31)}004\phantom{6}\\31\overline{)129}\\\phantom{31)}\underline{\phantom{}124\phantom{}}\\\phantom{31)99}5\\\end{array}
Find closest multiple of 31 to 129. We see that 4 \times 31 = 124 is the nearest. Now subtract 124 from 129 to get reminder 5. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }5
Since 5 is less than 31, stop the division. The reminder is 5. 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}