Evaluate
\frac{85}{62}\approx 1.370967742
Factor
\frac{5 \cdot 17}{2 \cdot 31} = 1\frac{23}{62} = 1.3709677419354838
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\begin{array}{l}\phantom{62)}\phantom{1}\\62\overline{)85}\\\end{array}
Use the 1^{st} digit 8 from dividend 85
\begin{array}{l}\phantom{62)}0\phantom{2}\\62\overline{)85}\\\end{array}
Since 8 is less than 62, use the next digit 5 from dividend 85 and add 0 to the quotient
\begin{array}{l}\phantom{62)}0\phantom{3}\\62\overline{)85}\\\end{array}
Use the 2^{nd} digit 5 from dividend 85
\begin{array}{l}\phantom{62)}01\phantom{4}\\62\overline{)85}\\\phantom{62)}\underline{\phantom{}62\phantom{}}\\\phantom{62)}23\\\end{array}
Find closest multiple of 62 to 85. We see that 1 \times 62 = 62 is the nearest. Now subtract 62 from 85 to get reminder 23. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }23
Since 23 is less than 62, stop the division. The reminder is 23. 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}