Evaluate
\frac{565}{12}\approx 47.083333333
Factor
\frac{5 \cdot 113}{2 ^ {2} \cdot 3} = 47\frac{1}{12} = 47.083333333333336
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)2825}\\\end{array}
Use the 1^{st} digit 2 from dividend 2825
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)2825}\\\end{array}
Since 2 is less than 60, use the next digit 8 from dividend 2825 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)2825}\\\end{array}
Use the 2^{nd} digit 8 from dividend 2825
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)2825}\\\end{array}
Since 28 is less than 60, use the next digit 2 from dividend 2825 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)2825}\\\end{array}
Use the 3^{rd} digit 2 from dividend 2825
\begin{array}{l}\phantom{60)}004\phantom{6}\\60\overline{)2825}\\\phantom{60)}\underline{\phantom{}240\phantom{9}}\\\phantom{60)9}42\\\end{array}
Find closest multiple of 60 to 282. We see that 4 \times 60 = 240 is the nearest. Now subtract 240 from 282 to get reminder 42. Add 4 to quotient.
\begin{array}{l}\phantom{60)}004\phantom{7}\\60\overline{)2825}\\\phantom{60)}\underline{\phantom{}240\phantom{9}}\\\phantom{60)9}425\\\end{array}
Use the 4^{th} digit 5 from dividend 2825
\begin{array}{l}\phantom{60)}0047\phantom{8}\\60\overline{)2825}\\\phantom{60)}\underline{\phantom{}240\phantom{9}}\\\phantom{60)9}425\\\phantom{60)}\underline{\phantom{9}420\phantom{}}\\\phantom{60)999}5\\\end{array}
Find closest multiple of 60 to 425. We see that 7 \times 60 = 420 is the nearest. Now subtract 420 from 425 to get reminder 5. Add 7 to quotient.
\text{Quotient: }47 \text{Reminder: }5
Since 5 is less than 60, stop the division. The reminder is 5. The topmost line 0047 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 47.
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}