Evaluate
\frac{50}{31}\approx 1.612903226
Factor
\frac{2 \cdot 5 ^ {2}}{31} = 1\frac{19}{31} = 1.6129032258064515
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\begin{array}{l}\phantom{1023000)}\phantom{1}\\1023000\overline{)1650000}\\\end{array}
Use the 1^{st} digit 1 from dividend 1650000
\begin{array}{l}\phantom{1023000)}0\phantom{2}\\1023000\overline{)1650000}\\\end{array}
Since 1 is less than 1023000, use the next digit 6 from dividend 1650000 and add 0 to the quotient
\begin{array}{l}\phantom{1023000)}0\phantom{3}\\1023000\overline{)1650000}\\\end{array}
Use the 2^{nd} digit 6 from dividend 1650000
\begin{array}{l}\phantom{1023000)}00\phantom{4}\\1023000\overline{)1650000}\\\end{array}
Since 16 is less than 1023000, use the next digit 5 from dividend 1650000 and add 0 to the quotient
\begin{array}{l}\phantom{1023000)}00\phantom{5}\\1023000\overline{)1650000}\\\end{array}
Use the 3^{rd} digit 5 from dividend 1650000
\begin{array}{l}\phantom{1023000)}000\phantom{6}\\1023000\overline{)1650000}\\\end{array}
Since 165 is less than 1023000, use the next digit 0 from dividend 1650000 and add 0 to the quotient
\begin{array}{l}\phantom{1023000)}000\phantom{7}\\1023000\overline{)1650000}\\\end{array}
Use the 4^{th} digit 0 from dividend 1650000
\begin{array}{l}\phantom{1023000)}0000\phantom{8}\\1023000\overline{)1650000}\\\end{array}
Since 1650 is less than 1023000, use the next digit 0 from dividend 1650000 and add 0 to the quotient
\begin{array}{l}\phantom{1023000)}0000\phantom{9}\\1023000\overline{)1650000}\\\end{array}
Use the 5^{th} digit 0 from dividend 1650000
\begin{array}{l}\phantom{1023000)}00000\phantom{10}\\1023000\overline{)1650000}\\\end{array}
Since 16500 is less than 1023000, use the next digit 0 from dividend 1650000 and add 0 to the quotient
\begin{array}{l}\phantom{1023000)}00000\phantom{11}\\1023000\overline{)1650000}\\\end{array}
Use the 6^{th} digit 0 from dividend 1650000
\begin{array}{l}\phantom{1023000)}000000\phantom{12}\\1023000\overline{)1650000}\\\end{array}
Since 165000 is less than 1023000, use the next digit 0 from dividend 1650000 and add 0 to the quotient
\begin{array}{l}\phantom{1023000)}000000\phantom{13}\\1023000\overline{)1650000}\\\end{array}
Use the 7^{th} digit 0 from dividend 1650000
\begin{array}{l}\phantom{1023000)}0000001\phantom{14}\\1023000\overline{)1650000}\\\phantom{1023000)}\underline{\phantom{}1023000\phantom{}}\\\phantom{1023000)9}627000\\\end{array}
Find closest multiple of 1023000 to 1650000. We see that 1 \times 1023000 = 1023000 is the nearest. Now subtract 1023000 from 1650000 to get reminder 627000. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }627000
Since 627000 is less than 1023000, stop the division. The reminder is 627000. The topmost line 0000001 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}