Evaluate
\frac{125}{23}\approx 5.434782609
Factor
\frac{5 ^ {3}}{23} = 5\frac{10}{23} = 5.434782608695652
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\begin{array}{l}\phantom{92)}\phantom{1}\\92\overline{)500}\\\end{array}
Use the 1^{st} digit 5 from dividend 500
\begin{array}{l}\phantom{92)}0\phantom{2}\\92\overline{)500}\\\end{array}
Since 5 is less than 92, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{92)}0\phantom{3}\\92\overline{)500}\\\end{array}
Use the 2^{nd} digit 0 from dividend 500
\begin{array}{l}\phantom{92)}00\phantom{4}\\92\overline{)500}\\\end{array}
Since 50 is less than 92, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{92)}00\phantom{5}\\92\overline{)500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 500
\begin{array}{l}\phantom{92)}005\phantom{6}\\92\overline{)500}\\\phantom{92)}\underline{\phantom{}460\phantom{}}\\\phantom{92)9}40\\\end{array}
Find closest multiple of 92 to 500. We see that 5 \times 92 = 460 is the nearest. Now subtract 460 from 500 to get reminder 40. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }40
Since 40 is less than 92, stop the division. The reminder is 40. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}