Evaluate
\frac{47}{40}=1.175
Factor
\frac{47}{2 ^ {3} \cdot 5} = 1\frac{7}{40} = 1.175
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)47}\\\end{array}
Use the 1^{st} digit 4 from dividend 47
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)47}\\\end{array}
Since 4 is less than 40, use the next digit 7 from dividend 47 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)47}\\\end{array}
Use the 2^{nd} digit 7 from dividend 47
\begin{array}{l}\phantom{40)}01\phantom{4}\\40\overline{)47}\\\phantom{40)}\underline{\phantom{}40\phantom{}}\\\phantom{40)9}7\\\end{array}
Find closest multiple of 40 to 47. We see that 1 \times 40 = 40 is the nearest. Now subtract 40 from 47 to get reminder 7. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }7
Since 7 is less than 40, stop the division. The reminder is 7. 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}