Evaluate
\frac{471}{56}\approx 8.410714286
Factor
\frac{3 \cdot 157}{2 ^ {3} \cdot 7} = 8\frac{23}{56} = 8.410714285714286
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\begin{array}{l}\phantom{56)}\phantom{1}\\56\overline{)471}\\\end{array}
Use the 1^{st} digit 4 from dividend 471
\begin{array}{l}\phantom{56)}0\phantom{2}\\56\overline{)471}\\\end{array}
Since 4 is less than 56, use the next digit 7 from dividend 471 and add 0 to the quotient
\begin{array}{l}\phantom{56)}0\phantom{3}\\56\overline{)471}\\\end{array}
Use the 2^{nd} digit 7 from dividend 471
\begin{array}{l}\phantom{56)}00\phantom{4}\\56\overline{)471}\\\end{array}
Since 47 is less than 56, use the next digit 1 from dividend 471 and add 0 to the quotient
\begin{array}{l}\phantom{56)}00\phantom{5}\\56\overline{)471}\\\end{array}
Use the 3^{rd} digit 1 from dividend 471
\begin{array}{l}\phantom{56)}008\phantom{6}\\56\overline{)471}\\\phantom{56)}\underline{\phantom{}448\phantom{}}\\\phantom{56)9}23\\\end{array}
Find closest multiple of 56 to 471. We see that 8 \times 56 = 448 is the nearest. Now subtract 448 from 471 to get reminder 23. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }23
Since 23 is less than 56, stop the division. The reminder is 23. 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}