Evaluate
\frac{45}{31}\approx 1.451612903
Factor
\frac{3 ^ {2} \cdot 5}{31} = 1\frac{14}{31} = 1.4516129032258065
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\begin{array}{l}\phantom{124)}\phantom{1}\\124\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{124)}0\phantom{2}\\124\overline{)180}\\\end{array}
Since 1 is less than 124, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{124)}0\phantom{3}\\124\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{124)}00\phantom{4}\\124\overline{)180}\\\end{array}
Since 18 is less than 124, use the next digit 0 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{124)}00\phantom{5}\\124\overline{)180}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{124)}001\phantom{6}\\124\overline{)180}\\\phantom{124)}\underline{\phantom{}124\phantom{}}\\\phantom{124)9}56\\\end{array}
Find closest multiple of 124 to 180. We see that 1 \times 124 = 124 is the nearest. Now subtract 124 from 180 to get reminder 56. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }56
Since 56 is less than 124, stop the division. The reminder is 56. The topmost line 001 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}