Evaluate
\frac{208}{115}\approx 1.808695652
Factor
\frac{2 ^ {4} \cdot 13}{5 \cdot 23} = 1\frac{93}{115} = 1.808695652173913
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\begin{array}{l}\phantom{460)}\phantom{1}\\460\overline{)832}\\\end{array}
Use the 1^{st} digit 8 from dividend 832
\begin{array}{l}\phantom{460)}0\phantom{2}\\460\overline{)832}\\\end{array}
Since 8 is less than 460, use the next digit 3 from dividend 832 and add 0 to the quotient
\begin{array}{l}\phantom{460)}0\phantom{3}\\460\overline{)832}\\\end{array}
Use the 2^{nd} digit 3 from dividend 832
\begin{array}{l}\phantom{460)}00\phantom{4}\\460\overline{)832}\\\end{array}
Since 83 is less than 460, use the next digit 2 from dividend 832 and add 0 to the quotient
\begin{array}{l}\phantom{460)}00\phantom{5}\\460\overline{)832}\\\end{array}
Use the 3^{rd} digit 2 from dividend 832
\begin{array}{l}\phantom{460)}001\phantom{6}\\460\overline{)832}\\\phantom{460)}\underline{\phantom{}460\phantom{}}\\\phantom{460)}372\\\end{array}
Find closest multiple of 460 to 832. We see that 1 \times 460 = 460 is the nearest. Now subtract 460 from 832 to get reminder 372. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }372
Since 372 is less than 460, stop the division. The reminder is 372. 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}