Evaluate
\frac{33}{8}=4.125
Factor
\frac{3 \cdot 11}{2 ^ {3}} = 4\frac{1}{8} = 4.125
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\begin{array}{l}\phantom{80)}\phantom{1}\\80\overline{)330}\\\end{array}
Use the 1^{st} digit 3 from dividend 330
\begin{array}{l}\phantom{80)}0\phantom{2}\\80\overline{)330}\\\end{array}
Since 3 is less than 80, use the next digit 3 from dividend 330 and add 0 to the quotient
\begin{array}{l}\phantom{80)}0\phantom{3}\\80\overline{)330}\\\end{array}
Use the 2^{nd} digit 3 from dividend 330
\begin{array}{l}\phantom{80)}00\phantom{4}\\80\overline{)330}\\\end{array}
Since 33 is less than 80, use the next digit 0 from dividend 330 and add 0 to the quotient
\begin{array}{l}\phantom{80)}00\phantom{5}\\80\overline{)330}\\\end{array}
Use the 3^{rd} digit 0 from dividend 330
\begin{array}{l}\phantom{80)}004\phantom{6}\\80\overline{)330}\\\phantom{80)}\underline{\phantom{}320\phantom{}}\\\phantom{80)9}10\\\end{array}
Find closest multiple of 80 to 330. We see that 4 \times 80 = 320 is the nearest. Now subtract 320 from 330 to get reminder 10. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }10
Since 10 is less than 80, stop the division. The reminder is 10. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}