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{99)}\phantom{1}\\99\overline{)165}\\\end{array}
Use the 1^{st} digit 1 from dividend 165
\begin{array}{l}\phantom{99)}0\phantom{2}\\99\overline{)165}\\\end{array}
Since 1 is less than 99, use the next digit 6 from dividend 165 and add 0 to the quotient
\begin{array}{l}\phantom{99)}0\phantom{3}\\99\overline{)165}\\\end{array}
Use the 2^{nd} digit 6 from dividend 165
\begin{array}{l}\phantom{99)}00\phantom{4}\\99\overline{)165}\\\end{array}
Since 16 is less than 99, use the next digit 5 from dividend 165 and add 0 to the quotient
\begin{array}{l}\phantom{99)}00\phantom{5}\\99\overline{)165}\\\end{array}
Use the 3^{rd} digit 5 from dividend 165
\begin{array}{l}\phantom{99)}001\phantom{6}\\99\overline{)165}\\\phantom{99)}\underline{\phantom{9}99\phantom{}}\\\phantom{99)9}66\\\end{array}
Find closest multiple of 99 to 165. We see that 1 \times 99 = 99 is the nearest. Now subtract 99 from 165 to get reminder 66. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }66
Since 66 is less than 99, stop the division. The reminder is 66. 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}