Evaluate
\frac{817}{622}\approx 1.313504823
Factor
\frac{19 \cdot 43}{2 \cdot 311} = 1\frac{195}{622} = 1.3135048231511255
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\begin{array}{l}\phantom{622)}\phantom{1}\\622\overline{)817}\\\end{array}
Use the 1^{st} digit 8 from dividend 817
\begin{array}{l}\phantom{622)}0\phantom{2}\\622\overline{)817}\\\end{array}
Since 8 is less than 622, use the next digit 1 from dividend 817 and add 0 to the quotient
\begin{array}{l}\phantom{622)}0\phantom{3}\\622\overline{)817}\\\end{array}
Use the 2^{nd} digit 1 from dividend 817
\begin{array}{l}\phantom{622)}00\phantom{4}\\622\overline{)817}\\\end{array}
Since 81 is less than 622, use the next digit 7 from dividend 817 and add 0 to the quotient
\begin{array}{l}\phantom{622)}00\phantom{5}\\622\overline{)817}\\\end{array}
Use the 3^{rd} digit 7 from dividend 817
\begin{array}{l}\phantom{622)}001\phantom{6}\\622\overline{)817}\\\phantom{622)}\underline{\phantom{}622\phantom{}}\\\phantom{622)}195\\\end{array}
Find closest multiple of 622 to 817. We see that 1 \times 622 = 622 is the nearest. Now subtract 622 from 817 to get reminder 195. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }195
Since 195 is less than 622, stop the division. The reminder is 195. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}