Evaluate
\frac{85}{63}\approx 1.349206349
Factor
\frac{5 \cdot 17}{3 ^ {2} \cdot 7} = 1\frac{22}{63} = 1.3492063492063493
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\begin{array}{l}\phantom{63)}\phantom{1}\\63\overline{)85}\\\end{array}
Use the 1^{st} digit 8 from dividend 85
\begin{array}{l}\phantom{63)}0\phantom{2}\\63\overline{)85}\\\end{array}
Since 8 is less than 63, use the next digit 5 from dividend 85 and add 0 to the quotient
\begin{array}{l}\phantom{63)}0\phantom{3}\\63\overline{)85}\\\end{array}
Use the 2^{nd} digit 5 from dividend 85
\begin{array}{l}\phantom{63)}01\phantom{4}\\63\overline{)85}\\\phantom{63)}\underline{\phantom{}63\phantom{}}\\\phantom{63)}22\\\end{array}
Find closest multiple of 63 to 85. We see that 1 \times 63 = 63 is the nearest. Now subtract 63 from 85 to get reminder 22. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }22
Since 22 is less than 63, stop the division. The reminder is 22. 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}