Evaluate
\frac{125}{84}\approx 1.488095238
Factor
\frac{5 ^ {3}}{2 ^ {2} \cdot 3 \cdot 7} = 1\frac{41}{84} = 1.4880952380952381
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\begin{array}{l}\phantom{168)}\phantom{1}\\168\overline{)250}\\\end{array}
Use the 1^{st} digit 2 from dividend 250
\begin{array}{l}\phantom{168)}0\phantom{2}\\168\overline{)250}\\\end{array}
Since 2 is less than 168, use the next digit 5 from dividend 250 and add 0 to the quotient
\begin{array}{l}\phantom{168)}0\phantom{3}\\168\overline{)250}\\\end{array}
Use the 2^{nd} digit 5 from dividend 250
\begin{array}{l}\phantom{168)}00\phantom{4}\\168\overline{)250}\\\end{array}
Since 25 is less than 168, use the next digit 0 from dividend 250 and add 0 to the quotient
\begin{array}{l}\phantom{168)}00\phantom{5}\\168\overline{)250}\\\end{array}
Use the 3^{rd} digit 0 from dividend 250
\begin{array}{l}\phantom{168)}001\phantom{6}\\168\overline{)250}\\\phantom{168)}\underline{\phantom{}168\phantom{}}\\\phantom{168)9}82\\\end{array}
Find closest multiple of 168 to 250. We see that 1 \times 168 = 168 is the nearest. Now subtract 168 from 250 to get reminder 82. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }82
Since 82 is less than 168, stop the division. The reminder is 82. 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}