Evaluate
\frac{1012}{53}\approx 19.094339623
Factor
\frac{2 ^ {2} \cdot 11 \cdot 23}{53} = 19\frac{5}{53} = 19.09433962264151
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\begin{array}{l}\phantom{53)}\phantom{1}\\53\overline{)1012}\\\end{array}
Use the 1^{st} digit 1 from dividend 1012
\begin{array}{l}\phantom{53)}0\phantom{2}\\53\overline{)1012}\\\end{array}
Since 1 is less than 53, use the next digit 0 from dividend 1012 and add 0 to the quotient
\begin{array}{l}\phantom{53)}0\phantom{3}\\53\overline{)1012}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1012
\begin{array}{l}\phantom{53)}00\phantom{4}\\53\overline{)1012}\\\end{array}
Since 10 is less than 53, use the next digit 1 from dividend 1012 and add 0 to the quotient
\begin{array}{l}\phantom{53)}00\phantom{5}\\53\overline{)1012}\\\end{array}
Use the 3^{rd} digit 1 from dividend 1012
\begin{array}{l}\phantom{53)}001\phantom{6}\\53\overline{)1012}\\\phantom{53)}\underline{\phantom{9}53\phantom{9}}\\\phantom{53)9}48\\\end{array}
Find closest multiple of 53 to 101. We see that 1 \times 53 = 53 is the nearest. Now subtract 53 from 101 to get reminder 48. Add 1 to quotient.
\begin{array}{l}\phantom{53)}001\phantom{7}\\53\overline{)1012}\\\phantom{53)}\underline{\phantom{9}53\phantom{9}}\\\phantom{53)9}482\\\end{array}
Use the 4^{th} digit 2 from dividend 1012
\begin{array}{l}\phantom{53)}0019\phantom{8}\\53\overline{)1012}\\\phantom{53)}\underline{\phantom{9}53\phantom{9}}\\\phantom{53)9}482\\\phantom{53)}\underline{\phantom{9}477\phantom{}}\\\phantom{53)999}5\\\end{array}
Find closest multiple of 53 to 482. We see that 9 \times 53 = 477 is the nearest. Now subtract 477 from 482 to get reminder 5. Add 9 to quotient.
\text{Quotient: }19 \text{Reminder: }5
Since 5 is less than 53, stop the division. The reminder is 5. The topmost line 0019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.
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}