Evaluate
\frac{311}{94}\approx 3.308510638
Factor
\frac{311}{2 \cdot 47} = 3\frac{29}{94} = 3.3085106382978724
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\begin{array}{l}\phantom{188)}\phantom{1}\\188\overline{)622}\\\end{array}
Use the 1^{st} digit 6 from dividend 622
\begin{array}{l}\phantom{188)}0\phantom{2}\\188\overline{)622}\\\end{array}
Since 6 is less than 188, use the next digit 2 from dividend 622 and add 0 to the quotient
\begin{array}{l}\phantom{188)}0\phantom{3}\\188\overline{)622}\\\end{array}
Use the 2^{nd} digit 2 from dividend 622
\begin{array}{l}\phantom{188)}00\phantom{4}\\188\overline{)622}\\\end{array}
Since 62 is less than 188, use the next digit 2 from dividend 622 and add 0 to the quotient
\begin{array}{l}\phantom{188)}00\phantom{5}\\188\overline{)622}\\\end{array}
Use the 3^{rd} digit 2 from dividend 622
\begin{array}{l}\phantom{188)}003\phantom{6}\\188\overline{)622}\\\phantom{188)}\underline{\phantom{}564\phantom{}}\\\phantom{188)9}58\\\end{array}
Find closest multiple of 188 to 622. We see that 3 \times 188 = 564 is the nearest. Now subtract 564 from 622 to get reminder 58. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }58
Since 58 is less than 188, stop the division. The reminder is 58. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}