Evaluate
\frac{83}{11}\approx 7.545454545
Factor
\frac{83}{11} = 7\frac{6}{11} = 7.545454545454546
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)166}\\\end{array}
Use the 1^{st} digit 1 from dividend 166
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)166}\\\end{array}
Since 1 is less than 22, use the next digit 6 from dividend 166 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)166}\\\end{array}
Use the 2^{nd} digit 6 from dividend 166
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)166}\\\end{array}
Since 16 is less than 22, use the next digit 6 from dividend 166 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)166}\\\end{array}
Use the 3^{rd} digit 6 from dividend 166
\begin{array}{l}\phantom{22)}007\phantom{6}\\22\overline{)166}\\\phantom{22)}\underline{\phantom{}154\phantom{}}\\\phantom{22)9}12\\\end{array}
Find closest multiple of 22 to 166. We see that 7 \times 22 = 154 is the nearest. Now subtract 154 from 166 to get reminder 12. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }12
Since 12 is less than 22, stop the division. The reminder is 12. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}