Evaluate
\frac{40000}{99}\approx 404.04040404
Factor
\frac{2 ^ {6} \cdot 5 ^ {4}}{3 ^ {2} \cdot 11} = 404\frac{4}{99} = 404.04040404040404
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\begin{array}{l}\phantom{1980)}\phantom{1}\\1980\overline{)800000}\\\end{array}
Use the 1^{st} digit 8 from dividend 800000
\begin{array}{l}\phantom{1980)}0\phantom{2}\\1980\overline{)800000}\\\end{array}
Since 8 is less than 1980, use the next digit 0 from dividend 800000 and add 0 to the quotient
\begin{array}{l}\phantom{1980)}0\phantom{3}\\1980\overline{)800000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 800000
\begin{array}{l}\phantom{1980)}00\phantom{4}\\1980\overline{)800000}\\\end{array}
Since 80 is less than 1980, use the next digit 0 from dividend 800000 and add 0 to the quotient
\begin{array}{l}\phantom{1980)}00\phantom{5}\\1980\overline{)800000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 800000
\begin{array}{l}\phantom{1980)}000\phantom{6}\\1980\overline{)800000}\\\end{array}
Since 800 is less than 1980, use the next digit 0 from dividend 800000 and add 0 to the quotient
\begin{array}{l}\phantom{1980)}000\phantom{7}\\1980\overline{)800000}\\\end{array}
Use the 4^{th} digit 0 from dividend 800000
\begin{array}{l}\phantom{1980)}0004\phantom{8}\\1980\overline{)800000}\\\phantom{1980)}\underline{\phantom{}7920\phantom{99}}\\\phantom{1980)99}80\\\end{array}
Find closest multiple of 1980 to 8000. We see that 4 \times 1980 = 7920 is the nearest. Now subtract 7920 from 8000 to get reminder 80. Add 4 to quotient.
\begin{array}{l}\phantom{1980)}0004\phantom{9}\\1980\overline{)800000}\\\phantom{1980)}\underline{\phantom{}7920\phantom{99}}\\\phantom{1980)99}800\\\end{array}
Use the 5^{th} digit 0 from dividend 800000
\begin{array}{l}\phantom{1980)}00040\phantom{10}\\1980\overline{)800000}\\\phantom{1980)}\underline{\phantom{}7920\phantom{99}}\\\phantom{1980)99}800\\\end{array}
Since 800 is less than 1980, use the next digit 0 from dividend 800000 and add 0 to the quotient
\begin{array}{l}\phantom{1980)}00040\phantom{11}\\1980\overline{)800000}\\\phantom{1980)}\underline{\phantom{}7920\phantom{99}}\\\phantom{1980)99}8000\\\end{array}
Use the 6^{th} digit 0 from dividend 800000
\begin{array}{l}\phantom{1980)}000404\phantom{12}\\1980\overline{)800000}\\\phantom{1980)}\underline{\phantom{}7920\phantom{99}}\\\phantom{1980)99}8000\\\phantom{1980)}\underline{\phantom{99}7920\phantom{}}\\\phantom{1980)9999}80\\\end{array}
Find closest multiple of 1980 to 8000. We see that 4 \times 1980 = 7920 is the nearest. Now subtract 7920 from 8000 to get reminder 80. Add 4 to quotient.
\text{Quotient: }404 \text{Reminder: }80
Since 80 is less than 1980, stop the division. The reminder is 80. The topmost line 000404 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 404.
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}