Evaluate
\frac{85}{58}\approx 1.465517241
Factor
\frac{5 \cdot 17}{2 \cdot 29} = 1\frac{27}{58} = 1.4655172413793103
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\begin{array}{l}\phantom{58)}\phantom{1}\\58\overline{)85}\\\end{array}
Use the 1^{st} digit 8 from dividend 85
\begin{array}{l}\phantom{58)}0\phantom{2}\\58\overline{)85}\\\end{array}
Since 8 is less than 58, use the next digit 5 from dividend 85 and add 0 to the quotient
\begin{array}{l}\phantom{58)}0\phantom{3}\\58\overline{)85}\\\end{array}
Use the 2^{nd} digit 5 from dividend 85
\begin{array}{l}\phantom{58)}01\phantom{4}\\58\overline{)85}\\\phantom{58)}\underline{\phantom{}58\phantom{}}\\\phantom{58)}27\\\end{array}
Find closest multiple of 58 to 85. We see that 1 \times 58 = 58 is the nearest. Now subtract 58 from 85 to get reminder 27. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }27
Since 27 is less than 58, stop the division. The reminder is 27. The topmost line 01 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}