Evaluate
\frac{72}{47}\approx 1.531914894
Factor
\frac{2 ^ {3} \cdot 3 ^ {2}}{47} = 1\frac{25}{47} = 1.5319148936170213
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\begin{array}{l}\phantom{47)}\phantom{1}\\47\overline{)72}\\\end{array}
Use the 1^{st} digit 7 from dividend 72
\begin{array}{l}\phantom{47)}0\phantom{2}\\47\overline{)72}\\\end{array}
Since 7 is less than 47, use the next digit 2 from dividend 72 and add 0 to the quotient
\begin{array}{l}\phantom{47)}0\phantom{3}\\47\overline{)72}\\\end{array}
Use the 2^{nd} digit 2 from dividend 72
\begin{array}{l}\phantom{47)}01\phantom{4}\\47\overline{)72}\\\phantom{47)}\underline{\phantom{}47\phantom{}}\\\phantom{47)}25\\\end{array}
Find closest multiple of 47 to 72. We see that 1 \times 47 = 47 is the nearest. Now subtract 47 from 72 to get reminder 25. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }25
Since 25 is less than 47, stop the division. The reminder is 25. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}