Evaluate
\frac{233}{28}\approx 8.321428571
Factor
\frac{233}{2 ^ {2} \cdot 7} = 8\frac{9}{28} = 8.321428571428571
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\begin{array}{l}\phantom{84)}\phantom{1}\\84\overline{)699}\\\end{array}
Use the 1^{st} digit 6 from dividend 699
\begin{array}{l}\phantom{84)}0\phantom{2}\\84\overline{)699}\\\end{array}
Since 6 is less than 84, use the next digit 9 from dividend 699 and add 0 to the quotient
\begin{array}{l}\phantom{84)}0\phantom{3}\\84\overline{)699}\\\end{array}
Use the 2^{nd} digit 9 from dividend 699
\begin{array}{l}\phantom{84)}00\phantom{4}\\84\overline{)699}\\\end{array}
Since 69 is less than 84, use the next digit 9 from dividend 699 and add 0 to the quotient
\begin{array}{l}\phantom{84)}00\phantom{5}\\84\overline{)699}\\\end{array}
Use the 3^{rd} digit 9 from dividend 699
\begin{array}{l}\phantom{84)}008\phantom{6}\\84\overline{)699}\\\phantom{84)}\underline{\phantom{}672\phantom{}}\\\phantom{84)9}27\\\end{array}
Find closest multiple of 84 to 699. We see that 8 \times 84 = 672 is the nearest. Now subtract 672 from 699 to get reminder 27. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }27
Since 27 is less than 84, stop the division. The reminder is 27. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}