Evaluate
\frac{80}{53}\approx 1.509433962
Factor
\frac{2 ^ {4} \cdot 5}{53} = 1\frac{27}{53} = 1.509433962264151
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\begin{array}{l}\phantom{53)}\phantom{1}\\53\overline{)80}\\\end{array}
Use the 1^{st} digit 8 from dividend 80
\begin{array}{l}\phantom{53)}0\phantom{2}\\53\overline{)80}\\\end{array}
Since 8 is less than 53, use the next digit 0 from dividend 80 and add 0 to the quotient
\begin{array}{l}\phantom{53)}0\phantom{3}\\53\overline{)80}\\\end{array}
Use the 2^{nd} digit 0 from dividend 80
\begin{array}{l}\phantom{53)}01\phantom{4}\\53\overline{)80}\\\phantom{53)}\underline{\phantom{}53\phantom{}}\\\phantom{53)}27\\\end{array}
Find closest multiple of 53 to 80. We see that 1 \times 53 = 53 is the nearest. Now subtract 53 from 80 to get reminder 27. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }27
Since 27 is less than 53, stop the division. The reminder is 27. The topmost line 01 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}