Evaluate
\frac{117}{20}=5.85
Factor
\frac{3 ^ {2} \cdot 13}{2 ^ {2} \cdot 5} = 5\frac{17}{20} = 5.85
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)117}\\\end{array}
Use the 1^{st} digit 1 from dividend 117
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)117}\\\end{array}
Since 1 is less than 20, use the next digit 1 from dividend 117 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)117}\\\end{array}
Use the 2^{nd} digit 1 from dividend 117
\begin{array}{l}\phantom{20)}00\phantom{4}\\20\overline{)117}\\\end{array}
Since 11 is less than 20, use the next digit 7 from dividend 117 and add 0 to the quotient
\begin{array}{l}\phantom{20)}00\phantom{5}\\20\overline{)117}\\\end{array}
Use the 3^{rd} digit 7 from dividend 117
\begin{array}{l}\phantom{20)}005\phantom{6}\\20\overline{)117}\\\phantom{20)}\underline{\phantom{}100\phantom{}}\\\phantom{20)9}17\\\end{array}
Find closest multiple of 20 to 117. We see that 5 \times 20 = 100 is the nearest. Now subtract 100 from 117 to get reminder 17. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }17
Since 17 is less than 20, stop the division. The reminder is 17. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}