Evaluate
\frac{631}{205}\approx 3.07804878
Factor
\frac{631}{5 \cdot 41} = 3\frac{16}{205} = 3.078048780487805
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\begin{array}{l}\phantom{615)}\phantom{1}\\615\overline{)1893}\\\end{array}
Use the 1^{st} digit 1 from dividend 1893
\begin{array}{l}\phantom{615)}0\phantom{2}\\615\overline{)1893}\\\end{array}
Since 1 is less than 615, use the next digit 8 from dividend 1893 and add 0 to the quotient
\begin{array}{l}\phantom{615)}0\phantom{3}\\615\overline{)1893}\\\end{array}
Use the 2^{nd} digit 8 from dividend 1893
\begin{array}{l}\phantom{615)}00\phantom{4}\\615\overline{)1893}\\\end{array}
Since 18 is less than 615, use the next digit 9 from dividend 1893 and add 0 to the quotient
\begin{array}{l}\phantom{615)}00\phantom{5}\\615\overline{)1893}\\\end{array}
Use the 3^{rd} digit 9 from dividend 1893
\begin{array}{l}\phantom{615)}000\phantom{6}\\615\overline{)1893}\\\end{array}
Since 189 is less than 615, use the next digit 3 from dividend 1893 and add 0 to the quotient
\begin{array}{l}\phantom{615)}000\phantom{7}\\615\overline{)1893}\\\end{array}
Use the 4^{th} digit 3 from dividend 1893
\begin{array}{l}\phantom{615)}0003\phantom{8}\\615\overline{)1893}\\\phantom{615)}\underline{\phantom{}1845\phantom{}}\\\phantom{615)99}48\\\end{array}
Find closest multiple of 615 to 1893. We see that 3 \times 615 = 1845 is the nearest. Now subtract 1845 from 1893 to get reminder 48. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }48
Since 48 is less than 615, stop the division. The reminder is 48. The topmost line 0003 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}