Evaluate
\frac{47}{8}=5.875
Factor
\frac{47}{2 ^ {3}} = 5\frac{7}{8} = 5.875
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\begin{array}{l}\phantom{24)}\phantom{1}\\24\overline{)141}\\\end{array}
Use the 1^{st} digit 1 from dividend 141
\begin{array}{l}\phantom{24)}0\phantom{2}\\24\overline{)141}\\\end{array}
Since 1 is less than 24, use the next digit 4 from dividend 141 and add 0 to the quotient
\begin{array}{l}\phantom{24)}0\phantom{3}\\24\overline{)141}\\\end{array}
Use the 2^{nd} digit 4 from dividend 141
\begin{array}{l}\phantom{24)}00\phantom{4}\\24\overline{)141}\\\end{array}
Since 14 is less than 24, use the next digit 1 from dividend 141 and add 0 to the quotient
\begin{array}{l}\phantom{24)}00\phantom{5}\\24\overline{)141}\\\end{array}
Use the 3^{rd} digit 1 from dividend 141
\begin{array}{l}\phantom{24)}005\phantom{6}\\24\overline{)141}\\\phantom{24)}\underline{\phantom{}120\phantom{}}\\\phantom{24)9}21\\\end{array}
Find closest multiple of 24 to 141. We see that 5 \times 24 = 120 is the nearest. Now subtract 120 from 141 to get reminder 21. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }21
Since 21 is less than 24, stop the division. The reminder is 21. 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}