Evaluate
\frac{271}{48}\approx 5.645833333
Factor
\frac{271}{2 ^ {4} \cdot 3} = 5\frac{31}{48} = 5.645833333333333
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\begin{array}{l}\phantom{48)}\phantom{1}\\48\overline{)271}\\\end{array}
Use the 1^{st} digit 2 from dividend 271
\begin{array}{l}\phantom{48)}0\phantom{2}\\48\overline{)271}\\\end{array}
Since 2 is less than 48, use the next digit 7 from dividend 271 and add 0 to the quotient
\begin{array}{l}\phantom{48)}0\phantom{3}\\48\overline{)271}\\\end{array}
Use the 2^{nd} digit 7 from dividend 271
\begin{array}{l}\phantom{48)}00\phantom{4}\\48\overline{)271}\\\end{array}
Since 27 is less than 48, use the next digit 1 from dividend 271 and add 0 to the quotient
\begin{array}{l}\phantom{48)}00\phantom{5}\\48\overline{)271}\\\end{array}
Use the 3^{rd} digit 1 from dividend 271
\begin{array}{l}\phantom{48)}005\phantom{6}\\48\overline{)271}\\\phantom{48)}\underline{\phantom{}240\phantom{}}\\\phantom{48)9}31\\\end{array}
Find closest multiple of 48 to 271. We see that 5 \times 48 = 240 is the nearest. Now subtract 240 from 271 to get reminder 31. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }31
Since 31 is less than 48, stop the division. The reminder is 31. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}