Evaluate
\frac{47}{9}\approx 5.222222222
Factor
\frac{47}{3 ^ {2}} = 5\frac{2}{9} = 5.222222222222222
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)282}\\\end{array}
Use the 1^{st} digit 2 from dividend 282
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)282}\\\end{array}
Since 2 is less than 54, use the next digit 8 from dividend 282 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)282}\\\end{array}
Use the 2^{nd} digit 8 from dividend 282
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)282}\\\end{array}
Since 28 is less than 54, use the next digit 2 from dividend 282 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)282}\\\end{array}
Use the 3^{rd} digit 2 from dividend 282
\begin{array}{l}\phantom{54)}005\phantom{6}\\54\overline{)282}\\\phantom{54)}\underline{\phantom{}270\phantom{}}\\\phantom{54)9}12\\\end{array}
Find closest multiple of 54 to 282. We see that 5 \times 54 = 270 is the nearest. Now subtract 270 from 282 to get reminder 12. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }12
Since 12 is less than 54, stop the division. The reminder is 12. 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}