Evaluate
\frac{254}{47}\approx 5.404255319
Factor
\frac{2 \cdot 127}{47} = 5\frac{19}{47} = 5.404255319148936
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\begin{array}{l}\phantom{47)}\phantom{1}\\47\overline{)254}\\\end{array}
Use the 1^{st} digit 2 from dividend 254
\begin{array}{l}\phantom{47)}0\phantom{2}\\47\overline{)254}\\\end{array}
Since 2 is less than 47, use the next digit 5 from dividend 254 and add 0 to the quotient
\begin{array}{l}\phantom{47)}0\phantom{3}\\47\overline{)254}\\\end{array}
Use the 2^{nd} digit 5 from dividend 254
\begin{array}{l}\phantom{47)}00\phantom{4}\\47\overline{)254}\\\end{array}
Since 25 is less than 47, use the next digit 4 from dividend 254 and add 0 to the quotient
\begin{array}{l}\phantom{47)}00\phantom{5}\\47\overline{)254}\\\end{array}
Use the 3^{rd} digit 4 from dividend 254
\begin{array}{l}\phantom{47)}005\phantom{6}\\47\overline{)254}\\\phantom{47)}\underline{\phantom{}235\phantom{}}\\\phantom{47)9}19\\\end{array}
Find closest multiple of 47 to 254. We see that 5 \times 47 = 235 is the nearest. Now subtract 235 from 254 to get reminder 19. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }19
Since 19 is less than 47, stop the division. The reminder is 19. 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}