Evaluate
\frac{20}{13}\approx 1.538461538
Factor
\frac{2 ^ {2} \cdot 5}{13} = 1\frac{7}{13} = 1.5384615384615385
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)100}\\\end{array}
Use the 1^{st} digit 1 from dividend 100
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)100}\\\end{array}
Since 1 is less than 65, use the next digit 0 from dividend 100 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)100}\\\end{array}
Use the 2^{nd} digit 0 from dividend 100
\begin{array}{l}\phantom{65)}00\phantom{4}\\65\overline{)100}\\\end{array}
Since 10 is less than 65, use the next digit 0 from dividend 100 and add 0 to the quotient
\begin{array}{l}\phantom{65)}00\phantom{5}\\65\overline{)100}\\\end{array}
Use the 3^{rd} digit 0 from dividend 100
\begin{array}{l}\phantom{65)}001\phantom{6}\\65\overline{)100}\\\phantom{65)}\underline{\phantom{9}65\phantom{}}\\\phantom{65)9}35\\\end{array}
Find closest multiple of 65 to 100. We see that 1 \times 65 = 65 is the nearest. Now subtract 65 from 100 to get reminder 35. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }35
Since 35 is less than 65, stop the division. The reminder is 35. 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}