Evaluate
\frac{47}{5}=9.4
Factor
\frac{47}{5} = 9\frac{2}{5} = 9.4
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\begin{array}{l}\phantom{600)}\phantom{1}\\600\overline{)5640}\\\end{array}
Use the 1^{st} digit 5 from dividend 5640
\begin{array}{l}\phantom{600)}0\phantom{2}\\600\overline{)5640}\\\end{array}
Since 5 is less than 600, use the next digit 6 from dividend 5640 and add 0 to the quotient
\begin{array}{l}\phantom{600)}0\phantom{3}\\600\overline{)5640}\\\end{array}
Use the 2^{nd} digit 6 from dividend 5640
\begin{array}{l}\phantom{600)}00\phantom{4}\\600\overline{)5640}\\\end{array}
Since 56 is less than 600, use the next digit 4 from dividend 5640 and add 0 to the quotient
\begin{array}{l}\phantom{600)}00\phantom{5}\\600\overline{)5640}\\\end{array}
Use the 3^{rd} digit 4 from dividend 5640
\begin{array}{l}\phantom{600)}000\phantom{6}\\600\overline{)5640}\\\end{array}
Since 564 is less than 600, use the next digit 0 from dividend 5640 and add 0 to the quotient
\begin{array}{l}\phantom{600)}000\phantom{7}\\600\overline{)5640}\\\end{array}
Use the 4^{th} digit 0 from dividend 5640
\begin{array}{l}\phantom{600)}0009\phantom{8}\\600\overline{)5640}\\\phantom{600)}\underline{\phantom{}5400\phantom{}}\\\phantom{600)9}240\\\end{array}
Find closest multiple of 600 to 5640. We see that 9 \times 600 = 5400 is the nearest. Now subtract 5400 from 5640 to get reminder 240. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }240
Since 240 is less than 600, stop the division. The reminder is 240. The topmost line 0009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}