Evaluate
\frac{115}{47}\approx 2.446808511
Factor
\frac{5 \cdot 23}{47} = 2\frac{21}{47} = 2.4468085106382977
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\begin{array}{l}\phantom{47)}\phantom{1}\\47\overline{)115}\\\end{array}
Use the 1^{st} digit 1 from dividend 115
\begin{array}{l}\phantom{47)}0\phantom{2}\\47\overline{)115}\\\end{array}
Since 1 is less than 47, use the next digit 1 from dividend 115 and add 0 to the quotient
\begin{array}{l}\phantom{47)}0\phantom{3}\\47\overline{)115}\\\end{array}
Use the 2^{nd} digit 1 from dividend 115
\begin{array}{l}\phantom{47)}00\phantom{4}\\47\overline{)115}\\\end{array}
Since 11 is less than 47, use the next digit 5 from dividend 115 and add 0 to the quotient
\begin{array}{l}\phantom{47)}00\phantom{5}\\47\overline{)115}\\\end{array}
Use the 3^{rd} digit 5 from dividend 115
\begin{array}{l}\phantom{47)}002\phantom{6}\\47\overline{)115}\\\phantom{47)}\underline{\phantom{9}94\phantom{}}\\\phantom{47)9}21\\\end{array}
Find closest multiple of 47 to 115. We see that 2 \times 47 = 94 is the nearest. Now subtract 94 from 115 to get reminder 21. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }21
Since 21 is less than 47, stop the division. The reminder is 21. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}