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{32)}\phantom{1}\\32\overline{)188}\\\end{array}
Use the 1^{st} digit 1 from dividend 188
\begin{array}{l}\phantom{32)}0\phantom{2}\\32\overline{)188}\\\end{array}
Since 1 is less than 32, use the next digit 8 from dividend 188 and add 0 to the quotient
\begin{array}{l}\phantom{32)}0\phantom{3}\\32\overline{)188}\\\end{array}
Use the 2^{nd} digit 8 from dividend 188
\begin{array}{l}\phantom{32)}00\phantom{4}\\32\overline{)188}\\\end{array}
Since 18 is less than 32, use the next digit 8 from dividend 188 and add 0 to the quotient
\begin{array}{l}\phantom{32)}00\phantom{5}\\32\overline{)188}\\\end{array}
Use the 3^{rd} digit 8 from dividend 188
\begin{array}{l}\phantom{32)}005\phantom{6}\\32\overline{)188}\\\phantom{32)}\underline{\phantom{}160\phantom{}}\\\phantom{32)9}28\\\end{array}
Find closest multiple of 32 to 188. We see that 5 \times 32 = 160 is the nearest. Now subtract 160 from 188 to get reminder 28. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }28
Since 28 is less than 32, stop the division. The reminder is 28. 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}