Evaluate
\frac{5}{3}\approx 1.666666667
Factor
\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667
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\begin{array}{l}\phantom{510)}\phantom{1}\\510\overline{)850}\\\end{array}
Use the 1^{st} digit 8 from dividend 850
\begin{array}{l}\phantom{510)}0\phantom{2}\\510\overline{)850}\\\end{array}
Since 8 is less than 510, use the next digit 5 from dividend 850 and add 0 to the quotient
\begin{array}{l}\phantom{510)}0\phantom{3}\\510\overline{)850}\\\end{array}
Use the 2^{nd} digit 5 from dividend 850
\begin{array}{l}\phantom{510)}00\phantom{4}\\510\overline{)850}\\\end{array}
Since 85 is less than 510, use the next digit 0 from dividend 850 and add 0 to the quotient
\begin{array}{l}\phantom{510)}00\phantom{5}\\510\overline{)850}\\\end{array}
Use the 3^{rd} digit 0 from dividend 850
\begin{array}{l}\phantom{510)}001\phantom{6}\\510\overline{)850}\\\phantom{510)}\underline{\phantom{}510\phantom{}}\\\phantom{510)}340\\\end{array}
Find closest multiple of 510 to 850. We see that 1 \times 510 = 510 is the nearest. Now subtract 510 from 850 to get reminder 340. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }340
Since 340 is less than 510, stop the division. The reminder is 340. 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}