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{208)}\phantom{1}\\208\overline{)320}\\\end{array}
Use the 1^{st} digit 3 from dividend 320
\begin{array}{l}\phantom{208)}0\phantom{2}\\208\overline{)320}\\\end{array}
Since 3 is less than 208, use the next digit 2 from dividend 320 and add 0 to the quotient
\begin{array}{l}\phantom{208)}0\phantom{3}\\208\overline{)320}\\\end{array}
Use the 2^{nd} digit 2 from dividend 320
\begin{array}{l}\phantom{208)}00\phantom{4}\\208\overline{)320}\\\end{array}
Since 32 is less than 208, use the next digit 0 from dividend 320 and add 0 to the quotient
\begin{array}{l}\phantom{208)}00\phantom{5}\\208\overline{)320}\\\end{array}
Use the 3^{rd} digit 0 from dividend 320
\begin{array}{l}\phantom{208)}001\phantom{6}\\208\overline{)320}\\\phantom{208)}\underline{\phantom{}208\phantom{}}\\\phantom{208)}112\\\end{array}
Find closest multiple of 208 to 320. We see that 1 \times 208 = 208 is the nearest. Now subtract 208 from 320 to get reminder 112. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }112
Since 112 is less than 208, stop the division. The reminder is 112. 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}