Evaluate
\frac{475}{58}\approx 8.189655172
Factor
\frac{5 ^ {2} \cdot 19}{2 \cdot 29} = 8\frac{11}{58} = 8.189655172413794
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\begin{array}{l}\phantom{58)}\phantom{1}\\58\overline{)475}\\\end{array}
Use the 1^{st} digit 4 from dividend 475
\begin{array}{l}\phantom{58)}0\phantom{2}\\58\overline{)475}\\\end{array}
Since 4 is less than 58, use the next digit 7 from dividend 475 and add 0 to the quotient
\begin{array}{l}\phantom{58)}0\phantom{3}\\58\overline{)475}\\\end{array}
Use the 2^{nd} digit 7 from dividend 475
\begin{array}{l}\phantom{58)}00\phantom{4}\\58\overline{)475}\\\end{array}
Since 47 is less than 58, use the next digit 5 from dividend 475 and add 0 to the quotient
\begin{array}{l}\phantom{58)}00\phantom{5}\\58\overline{)475}\\\end{array}
Use the 3^{rd} digit 5 from dividend 475
\begin{array}{l}\phantom{58)}008\phantom{6}\\58\overline{)475}\\\phantom{58)}\underline{\phantom{}464\phantom{}}\\\phantom{58)9}11\\\end{array}
Find closest multiple of 58 to 475. We see that 8 \times 58 = 464 is the nearest. Now subtract 464 from 475 to get reminder 11. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }11
Since 11 is less than 58, stop the division. The reminder is 11. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}