Evaluate
\frac{92}{47}\approx 1.957446809
Factor
\frac{2 ^ {2} \cdot 23}{47} = 1\frac{45}{47} = 1.9574468085106382
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\begin{array}{l}\phantom{47)}\phantom{1}\\47\overline{)92}\\\end{array}
Use the 1^{st} digit 9 from dividend 92
\begin{array}{l}\phantom{47)}0\phantom{2}\\47\overline{)92}\\\end{array}
Since 9 is less than 47, use the next digit 2 from dividend 92 and add 0 to the quotient
\begin{array}{l}\phantom{47)}0\phantom{3}\\47\overline{)92}\\\end{array}
Use the 2^{nd} digit 2 from dividend 92
\begin{array}{l}\phantom{47)}01\phantom{4}\\47\overline{)92}\\\phantom{47)}\underline{\phantom{}47\phantom{}}\\\phantom{47)}45\\\end{array}
Find closest multiple of 47 to 92. We see that 1 \times 47 = 47 is the nearest. Now subtract 47 from 92 to get reminder 45. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }45
Since 45 is less than 47, stop the division. The reminder is 45. 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}