Evaluate
\frac{103}{20}=5.15
Factor
\frac{103}{2 ^ {2} \cdot 5} = 5\frac{3}{20} = 5.15
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)103}\\\end{array}
Use the 1^{st} digit 1 from dividend 103
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)103}\\\end{array}
Since 1 is less than 20, use the next digit 0 from dividend 103 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)103}\\\end{array}
Use the 2^{nd} digit 0 from dividend 103
\begin{array}{l}\phantom{20)}00\phantom{4}\\20\overline{)103}\\\end{array}
Since 10 is less than 20, use the next digit 3 from dividend 103 and add 0 to the quotient
\begin{array}{l}\phantom{20)}00\phantom{5}\\20\overline{)103}\\\end{array}
Use the 3^{rd} digit 3 from dividend 103
\begin{array}{l}\phantom{20)}005\phantom{6}\\20\overline{)103}\\\phantom{20)}\underline{\phantom{}100\phantom{}}\\\phantom{20)99}3\\\end{array}
Find closest multiple of 20 to 103. We see that 5 \times 20 = 100 is the nearest. Now subtract 100 from 103 to get reminder 3. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }3
Since 3 is less than 20, stop the division. The reminder is 3. 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}