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{23)}\phantom{1}\\23\overline{)125}\\\end{array}
Use the 1^{st} digit 1 from dividend 125
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)125}\\\end{array}
Since 1 is less than 23, use the next digit 2 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)125}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125
\begin{array}{l}\phantom{23)}00\phantom{4}\\23\overline{)125}\\\end{array}
Since 12 is less than 23, use the next digit 5 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{23)}00\phantom{5}\\23\overline{)125}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125
\begin{array}{l}\phantom{23)}005\phantom{6}\\23\overline{)125}\\\phantom{23)}\underline{\phantom{}115\phantom{}}\\\phantom{23)9}10\\\end{array}
Find closest multiple of 23 to 125. We see that 5 \times 23 = 115 is the nearest. Now subtract 115 from 125 to get reminder 10. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }10
Since 10 is less than 23, stop the division. The reminder is 10. 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}